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1.
Seaweed is found under 80 m deep seafloor. To reach it, a diver makes a 45° dive from a boat. What is the distance travelled by the diver to reach the seafloor?
80 m
80.2 m
80√2 m
80√3 m
2.
A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground, then the height of pole, if the angle made by the rope with the ground level is 30°, is
5 m
10 m
15 m
20 m
3.
If the height of the tower is equal to the length of its shadow, then the angle of elevation of the Sun is
30°
45°
60°
90°
4.
From a point on the ground which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 60°. The height (in metres) of the tower is
10\(\sqrt{3}\)
30\(\sqrt{3}\)
60
30
5.
A spherical balloon of radius r subtends an angle eat the eye of the observer. If the angle of elevation of its centre is Φ, then the height of the centre of balloon is
r sin Φ/2 cos θ
r sin Φ cosec θ
r sin Φ cosec θ/2
None of these
6.
A ladder rests against a vertical wall at an inclination a to the horizontal. If its foot is pulled away from the wall through a distance p, so that its upper end slides at distance down the wall and then the ladder makes an angle β to the horizontal, then \(\frac{\cos \beta-\cos \alpha}{\sin \alpha-\sin \beta}\) is equal to
p / a
p / q
qp
1 / pq
7.
If the angle of elevation of a cloud from a point h m above a lake is a and angle of depression of its reflection in the take is β. Then the height of the cloud is
\(\frac{h(\tan \beta+\tan \alpha)}{\tan \beta-\tan \alpha} \mathrm{m}\)
\(\frac{h(\tan \beta-\tan \alpha)}{\tan \beta+\tan \alpha} \mathrm{m}\)
\(\frac{h \tan \beta+\tan \alpha}{\tan \beta-\tan \alpha}\)
\(\frac{h \tan \beta-\tan \alpha}{\tan \beta+\tan \alpha}\)
8.
First, plot the points A(2, 4), B (6, 4), C (6,2) and 0 (2,2) and join all adjacent points. A pole BE of height his standing on point B. If Angle of elevation of the top of a pole from point A is 30°, The total area formed by the
figure is
\(8(\sqrt{3}+1) m^{2}\)
\(8(\sqrt{3}-1) m^{2}\)
\(\frac{8(\sqrt{3}+1)}{\sqrt{3}} \mathrm{~m}^{2}\)
\(\frac{8(\sqrt{3}-1)}{\sqrt{3}} m^{2}\)
9.
In the following figure, from the top of a building AB, 60 m high, the angles of depression of the top and the bottom of a vertical lamp post CD are observed to be 30° and 60°, respectively.
Find the radius of the circle, if Y-axis and AB are the tangents to the circle.
20 m
15 m
10 m
5 m
10.
In the following figure, from the top of a building AB, 60 m high, the angles of depression of the top and the bottom of a vertical lamp post CD are observed to be 30° and 60°, respectively.
Find the height of the lamp post CD.
60 m
40 m
20 m
10 m
11.
In the following figure, from the top of a building AB, 60 m high, the angles of depression of the top and the bottom of a vertical lamp post CD are observed to be 30° and 60°, respectively.
Find the horizontal distance between BA and CO.
60\(\sqrt3\)m
40\(\sqrt3\)m
20\(\sqrt3\)m
10\(\sqrt3\)m
12.
A tower stands at the centre of a circular park. If A and B are two points on the boundary of the park, such that AB = a m subtends an angle of 60° at the foot of the tower and the angle of elevation of the top of the tower from A or B is 30°. Find, then the height of the tower is
\(\sqrt{3}\) a m
\(a / \sqrt{3} m\)
\(\frac{\sqrt{3}}{a} m\)
None of these
13.
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high. building are 45° and 60° respectively, then the height of the tower is
14.64 m
28.64 m
38.64 m
19.64 m
14.
The angles of elevation of the top of a tower from the points P and Q, at distance of a and b respectively from the base and in the same straight line with it, are complementary. The height of the tower is
ab
\(\sqrt{a b}\)
\(\sqrt{\frac{a}{b}}\)
\(\sqrt{\frac{b}{a}}\)
15.
A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 9.5 m away from the wall. The length of the ladder is
10 m
16 m
18 m
19 m
16.
A kite is flying at a height of 80 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with ground is 60°, then the length of the string is
62.37 m
92.37 m
52.57 m
72.57 m
17.
From the top of a 7 m high building the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°, then the height of the tower is
14.124 m
17.124 m
19.124 m
15.124 m
18.
A tree 6 m tall cast a 4m long shadow. At the same time, a flag pole cast a shadow 50 m long. How long is the flag pole?
75 m
100 m
150 m
50 m
19.
An observer, 1.5 m tall is 20.5 away from a tower 22 m high, then the angle of elevation of the top of the tower from the eye of the observer is
30°
45°
60°
90°
20.
The top of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, then the length of the wire is
12 m
10 m
8 m
6 m
21.
The length of a string between a kite and a point on the ground is 85 m. If the string makes an angle θ with level ground such that tan \(\theta=\frac{15}{8}\) then the height of kite is
75 m
78.05 m
226 m
None of these
22.
A circle artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground, then the height of pole, if the angle made by the rope with the ground level is 30°, is
5 m
10 m
15 m
20 m
23.
If sun’s elevation is 60° then a pole of height 6 m will cast a shadow of length
3√2 m
2√3 m
6√3 m
√3 m
24.
If the angle of the top of the 200 m high tower from a point C on the ground is 30°. The distance of the point C from the foot of the tower is (Take √3 = 1.732)
346.4 m
173.6 m
300.4 m
246.6 m
25.
In the given figure, the respective values of y and x are
60° and 30°
45° and 60°
60° and 45°
30° and 45°
26.
Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?
50 (√3 + 1) m2
50 √3 m2
50 m2
100 m2
27.
The angle of depression from the top of a tower 12 m high, at a point on the ground is 30°. The distance of the point from the top of the tower is:
12√3 m
24 m
6 m
12 m
28.
A ladder leaning against a wall makes an angle of 60° with the wall. If its foot is 6.2 m away from the wall, its length is
10.2 m
8 m
14.2 m
12.4 m
29.
Consider a ship with a right triangular mast. If the base of the mast is 10 m long, and the angle that the mast makes with the base is 60°, then what area of cloth is used to make the mast?
50 (√3 + 1) m2
50 √3 m2
50 m2
100 m2
30.
A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at 60° to the horizontal. The length of the string to the nearest metre is
55 m
87 m
100 m
60 m
31.
The ——– is the line drawn from the eye of an observer to the point in the object viewed by the observer
Line of sight
Line of sight propagation
Line of symmetry
Line of incidence
32.
A man on a top of a tower observes a truck at an angle of depression α where tanα = 1/ √5 and sees that it is moving towards the base of the tower. Ten minutes later, the angle of depression of the truck is found to be β where tan β = √5 . If the truck is moving at a uniform speed, then how much more time it will take to reach the base of the tower.
150√5 sec
1500 sec
150 sec
150/ √5 sec
33.
The angle of elevation from a point 30 feet from the base of a pole, of height h, as level ground to the top of the pole is 45° degree. Which equation can be used to find the height of the pole.
tan 45° = 30/h
tan 45° = h/30
sin 45° = h/30
cos 45° = h/30
34.
A man has to clean a window at a height of 5 m on a building. He needs to reach a point 1.3m below the window to clean it. What should be the length of the ladder that he should use which, when inclined at an angle of 60° to the horizontal, would enable him to reach the required position?
2.46
2√3
2.46/ √3
2.46√3
35.
A tree is broken by wind and its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of 45° with the ground. The entire length of the tree is
20 m
10 (1 + √2) m
10√2 m
10 m
36.
Consider a ladder which makes an angle of 60° with a wall of height 10 m and its top just touches the top of the wall. If the ladder is now rotated in such a way that its top now touches the top of the opposite wall which has a height of 10/√3 m. What is the angle by which the ladder is rotated.
45°
60°
90°
30°
37.
A 20 m long ladder touches the wall at a height of 10 m. The angle which the ladder makes with the horizontal is
30°
45°
60°
90°
38.
The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m.) is:
75√3
25√3
150
50√3
39.
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.
20
40√3
20√3
40
40.
In the following figure α is
Angle of Depression
Angle of incidence
Angle of Elevation
Angle of sight
41.
A tower stands vertically on the ground from a point on the ground which is 15 m away from the foot of tower. If the height of tower is 15√3 meters find the angle of elevation
30°
60°
90°
120°
42.
A tower stands vertically on the ground from a point on the ground which is 25 m away from the foot of tower if the height of tower is 25√3 metres find the angle of elevation.
120°
90°
60°
30°
43.
A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance of 30 metres from the foot of the tree. The height of the tree in metres is
35√3
40√3
25√3
30√3
44.
Consider a constellation of 3 stars A, B and C forming a right triangle with angle ABC = 90° and angle BAC = 30° . If the distance between star A and B is 3√3 x 1013 km, then how much time does light take to travel from star C to B with a speed of 3 x 108 m/s?
√3 x 105 sec
104 sec
√3 x 104 sec
105 sec
45.
The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 60 m then, the height of the first tower is
139.5 m
142 m
135 m
140.83 m
46.
A vertical tower is 20 m high. A man at some distance from the tower knows that the cosine of the angle of the elevation of the top of tower is 0.5. He is standing from the foot of the tower at a distance of:
30√3 m
20√3 m
20/√3 m
10/√3 m
47.
The length of shadow of a tower on the plane ground is √3 times the height of the tower. The angle of elevation of sun is :
90o
60o
30o
45o
48.
The angles of elevation of the top of a cliff from two points x and y metres from the base and in the same straight line with it are complementary. The height of the cliff is
\(x\sqrt { _{ ym } } m\)
\(\sqrt { x } y\quad m\)
\(\sqrt { XY } m\)
xy m
49.
If altitude of the sun is 60°, the height of a tower which casts a shadow of length 30 m is:
30√3 cm
30/√3 m
15 m
15√2 m
50.
The angle formed by the line of sight with the horizontal, when the point being viewed is above the horizontal level is called:
Obtuse angle
Angle of elevation
Angle of depression
Vertical angle
51.
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower is
30 m
20 m
40 m
10 m
52.
If the angles of depression from the top of a tower of height 40 m to the top and bottom of a tree are 45° and 60° respectively, then the height of the tree is
\(\frac { 40 }{ 3 } (3-\sqrt { 3 } )\)
\(\frac { 20 }{ 3 } (\sqrt { 3 } +3)\)
\(\frac { 20 }{ 3 } (\sqrt { 3 } +1)\)
\(\frac { 40 }{ 3 } (\sqrt { 3 } -1)\)
53.
The figure shows the observation of point C from point A. The angle of depression from A is:
30°
60°
75°
45°
54.
The ratio of the length of rod and its shadow is 1:√3, then the angle of elevation of the sun is:
45°
60°
90°
30°
55.
A tower stands vertically on the ground. From a point on the ground 30 m away from the foot of the tower, the angle of elevation of the top of the tower is 45°. The height of the tower will be
30√3 m
30 m
40 m
40√3 m
56.
If the angle of elevation of a cloud from a point 100 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is
200 m
30 m
500 m
100 m
57.
A man has a height of 1.732 m. He observes the angle of depression to the head and toe of his son as 30° and 60° respectively. What is the height of his son? (Take √3 = 1.732)
3 m
1.155 m
3.464 m
1.732 m
58.
An electrician has to repair an electric fault on a pole of height 4 m. He needs to reach a point 1.3 m below the top of the pole to undertake the repair work. The length of the ladder he should use which when inclined at an angle of 60° to the horizontal would enable him to reach the required position is:
\(\frac { 9\sqrt { 3 } }{ 5 } \)m
\(\frac { 5 }{ 9 } \)m
\(\frac { \sqrt { 3 } }{ 5 } \)m
\(\frac { 9 }{ 5 } \)m
59.
Two pillars are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the taller pillar is
a√2m
2a m
a m
a/√2 m
60.
In the above fig Q and α respectively are
Angle of Depression and Angle of Depression
Angle of Elevation and Angle of depression
Angle of Elevation and Angle of Elevation
Angle of depression and Angle of Elevation
61.
Find AB in the given figure
√3
30√3
20√3
10√3
62.
A tower stands vertically on the ground. From a point C on the ground, which is 20 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45°. The height of the tower is
10 m
8 m
15 m
20 m
63.
From the given figure, find h
√3 m
25√3m
50√3 m
2 √3 m
64.
If the height and length of the shadow of a man are the same, then the angle of elevation of the sun is
60°
45°
30°
15°
65.
A man is standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 600 and angle of depression of the base of the hill as 300. What is the height of the hill?
32 m
24√3 m
24m
8√3 m
66.
A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 450. The height of the tree is:
4.5 m
3 m
5.2 m
4 m
67.
A kite is flying, attached to a thread which is 165m long. The thread makes an angle of 300 with the ground. The height of the kite from the ground, assuming that there is no slack in the thread is
84 m
82.5 m
81.5 m
80 m
68.
Which of the following is rational?
√3 + √5
√4 + √9
√2 + √4
√6 + √9
1.
(c)
80√2 m
2.
(c)
15 m
3.
(b)
45°
4.
(d)
30
5.
(c)
r sin Φ cosec θ/2
6.
(b)
p / q
7.
(a)
\(\frac{h(\tan \beta+\tan \alpha)}{\tan \beta-\tan \alpha} \mathrm{m}\)
8.
(c)
\(\frac{8(\sqrt{3}+1)}{\sqrt{3}} \mathrm{~m}^{2}\)
9.
(d)
5 m
10.
(b)
40 m
11.
(c)
20\(\sqrt3\)m
12.
(b)
\(a / \sqrt{3} m\)
13.
(a)
14.64 m
14.
(b)
\(\sqrt{a b}\)
15.
(d)
19 m
16.
(b)
92.37 m
17.
(c)
19.124 m
18.
(a)
75 m
19.
(b)
45°
20.
(a)
12 m
21.
(a)
75 m
22.
(b)
10 m
23.
(b)
2√3 m
24.
(a)
346.4 m
25.
(a)
60° and 30°
26.
(b)
50 √3 m2
27.
(b)
24 m
28.
(d)
12.4 m
29.
(b)
50 √3 m2
30.
(b)
87 m
31.
(a)
Line of sight
32.
(c)
150 sec
33.
34.
35.
(b)
10 (1 + √2) m
36.
(c)
90°
37.
(a)
30°
38.
(a)
75√3
39.
(c)
20√3
40.
(c)
Angle of Elevation
41.
(b)
60°
42.
(c)
60°
43.
(d)
30√3
44.
(b)
104 sec
45.
(d)
140.83 m
46.
(c)
20/√3 m
47.
(c)
30o
48.
(c)
\(\sqrt { XY } m\)
49.
(a)
30√3 cm
50.
(b)
Angle of elevation
51.
(a)
30 m
52.
(a)
\(\frac { 40 }{ 3 } (3-\sqrt { 3 } )\)
53.
(a)
30°
54.
(d)
30°
55.
(b)
30 m
56.
(d)
100 m
57.
(b)
1.155 m
58.
(a)
\(\frac { 9\sqrt { 3 } }{ 5 } \)m
59.
(a)
a√2m
60.
(d)
Angle of depression and Angle of Elevation
61.
(c)
20√3
62.
(d)
20 m
63.
(b)
25√3m
64.
(b)
45°
65.
(a)
32 m
66.
(d)
4 m
67.
(b)
82.5 m
68.
(b)
√4 + √9
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