- A vertical pole is high and the length of its shadow is . What is the angle of elevation of the sun at that moment?
- A man tall observes that the angle of elevation of the top of a tree at a distance of from him is . What is the height of the tree?
- At the top of a cliff high, the angle of depression of a boat is . How far is the boat from the cliff?
- A ladder leaning against a vertical wall makes an angle of with the wall. Its foot is from the wall. Find its length.
- A kite flying at a height of is attached to a fully stretched string inclined at an angle of to the horizontal. Find the length of the string.
- When the angle between the ground and the suñ is , flag pole casts a . shadow of long. Find the height of the top of the flag.

360 A Texbook of Algebra and Trigononetry - A plane flying directly above a post away from an anti-aircraft gun observes the gun at an angle of depression of . Find the height of the plane.

- A man on the top of a high light-house is in line with two ships on the same side of it, whose angles of depression from the man are and respecting. Find the distance between the ships.
- and are two points in line with a tree. If the distance between and be and the angles of elevation of the top of the tree at and be and respectively, find the height of the tree.
- Two men are on the opposite sides of a high tower. If the measures of the angles of elevation of the top of the tower are and 22 respectively find the distance between them.
- A man standing away from a tower notices that the angles of elevation of the top and the bottom of a flag staff on the top of the tower are and respectively. Find the length of the flag staff.
- The angle of elevation of the top of a high tower from a point , on the same level as the foot of the tower, is . Find the angle of elevation of the top of the tower from a point nearer to from the foot of the tower.
- Two buildings and are apart. The angle of elevation from the top of the building to the top of the building is . The angle of elevation from the base of the building to the top of the building is . Find the height of the building .
- A window washer is working in a hotel building. An observer at a distance of from the building finds the angle of elevation of the worker to be of . The worker climbs up and the observer moves farther away from the building. Find the new angle of elevation of the worker.
- A man standing on the bank of a canal observes that the measure of the angle of elevation of a tree on the other side of the canal, is . On retreating 40 meters from the bank, he finds the measure of the angle of elevation of the tree as . Find the height of the tree and the width of the canal.

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