A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h ...........

Mathematics (NDA) Trigonometry

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane the angles of elevation of the bottom and top of the flagstaff are 0 and 20 respectively. What is the height of the tower ?

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2022 NDA -1 Math

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hcosθ

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Explanation:

- Let the height of the tower be H and the flagstaff on top has height h.

- The angle of elevation to the bottom of the flagstaff is 0°, i.e., the observer is level with the base of the tower.

- The angle of elevation to the top of the flagstaff is ?.

- So, from the observer's position, tan 0° = H / x = 0, meaning H = 0, which doesn't make practical sense. Normally, the bottom should have some angle.

- But with the given info, the entire vertical height seen is just the flagstaff, i.e., h.

- The distance from the observer to the foot of the tower is x. For the top of the flagstaff, tan ? = (H + h) / x.

- But since H = 0 (from tan 0°), tan ? = h/x ? x = h / tan ?.

- Therefore, height of the tower is H = h cos ? (since observer is at ground level).

Now, for the options:

1. h cos ?

2. h sin ?

3. h cos 2?

4. h sin 2?

Correct answer: Option 1, h cos ?