Trigonometry Height and Distance | Learn Mathematics Online

Trigonometry Height and Distance

Study Material (PDF)

Study Material (PDF)

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Question No: #1

If the angle of elevation of the sun increases from 45° to 60°, then the length of the shadow of a pillar is decreased by 60 m. Find the height of the pillar.

Ans: 7.1 m (approx)

Question No: #2

If the angle of elevation of the Sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60 m. Find the height of the pillar.

Ans: 81.96 m (approx)

Question No: #3

There is a bridge perpendicular to the river bank. If you go some distance from one side of the bridge along the river bank, the other end of the bridge is seen at an angle of 45° and if you move another 400 meters along the bank, that end is seen at an angle of 30°. Find the length of the bridge.

Ans: 200(√3+1) m

Question No: #4

There is a flagpole on a memorial monument. When the angle of elevation of the Sun is 30°, the shadow length of the flagpole is 3√3 meters. What is the height of the flagpole?

Ans: 3 m

Question No: #5

A pole of 126 decimeters high tilted slightly above the ground and its top point touched the ground at an angle of 30°. How high is the pole twisted?

Ans: 42 decimeters

Question No: #6

A telegraph post is bent at a point above the ground due to storm. Its top just meets the ground at a distance of 8√3 meters from its foot and makes an angle of 30° with the horizontal. Then find the height at which the post is bent. Also find its total height.

Ans: 8 m, 24 m

Question No: #7

The heights of two towers are 180 meters and 60 meters respectively. If the angle of elevation of the top of the first tower from the base of the second tower is 60°, what is the angle of elevation of the top of the second tower from the base of the first tower.

Ans: `30°`

Question No: #8

The height of the two pillars is `h_1` m and `h_2` m respectively. If the angle of elevation of the first peak from the base of the second pillar is 60° and the angle of elevation of the second peak from the base of the first is 30°, show that the height of the first pillar is three times the height of the second.

Ans:

Question No: #9

The ratio of the height of the two pillars is 1:3. If the angle of elevation from the foot of the smaller pillar to the peak of the larger pillar is 60°, what is the angle of elevation from the foot of the larger pillar to the pinnacle of the smaller pillar?

Ans: 30°

Question No: #10

The heights of two towers are `h_1` meter and `h_2` meter. If the angle of elevation of the top of the first tower from the foot of the second tower is 60° and the angle of elevation of the second tower from the foot of the first tower is 45°, then prove that `h_1^2 = 3h_2^2`

Ans:

1
2
3
4