Trigonometry Height and Distance

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #21

The angle of elevation of the top of an unfinished pillar from a point 150 meters away from its base is 45°. Calculate the height of the pillar that must be raised so that its new angle of elevation from the same point be 60°.
Ans: 109.8 m
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Question No: #22

The length of the flag at the roof of three-storied building is 3.3 meters. From any point of road, the angles of elevation of the top and foot of the flag-post are 50° and 45°. Calculate the height of three-storied building. [tan 50° = 1.192]
Ans: 17.19 m (approx)
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Question No: #23

There is an `h` meter high flag bar on a pillar. If the angle of elevation of the top and foot of the flag bar from any point on the ground is `\alpha` and `\beta` respectively, what is the height of the pillar?
Ans: `\frac{h tan \beta}{tan \alpha - tan \beta}`
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Question No: #24

A vertical pillar of height `h` cm stands on the plane ground. At a fixed point on the plane ground the height of the top of the pillar and that of a point `x` cm below the top subtend angles 60° and 30° respectively. Prove that `x = \frac{2h}{3}`

Question No: #25

Two pillars of equal heights stand on either side of a road which is 150 m wide. At a point on the road between the pillars, the angles of elevation of the top of the pillars are 60° and 30°. Find the height of each pillar.
Ans: `\frac{75\sqrt{3}}{2}` m
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Question No: #26

The distance between two pillars is 120√2 meters. The height of one pillar is twice the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. Find the height of the pillars.
Ans: 60 m, 120 m
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Question No: #27

The distance between two pillars is 150 meters. The height of one pillar is thrice the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. Find the height of the smaller pillar.
Ans: `25\sqrt{3}` m
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Question No: #28

From a side of a river of 600 meters wide, two boats start in two different directions to reach the opposite side of the river. The first boat moves making an angle of 30° with this bank and the second boat moves making an angle 90° with direction of the first boat. What will be the distance between the two boats when both of them reach the other side?​
Ans: 1385.6 m (approx)
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Question No: #29

ABCD is a rectangular field. In one corner A of the field there is a vertical rod. If the angles of elevation of the top of the rod from B, C and D are `\alpha, \beta, \gamma` respectively. Then show that, `cot^2 \alpha + cot^2 \gamma = \cot^2 \beta`.

Question No: #30

The angles of elevation of the top of a tower from two points at distances `d_1` and `d_2` units from the base and in the same straight line with it, are complementary. Prove that the height of the tower is `\sqrt{d_1 d_2}` unit.