Some Applications of Trigonometry

A tree casts a shadow 15 m long when the angle of elevation of the sun is 30°. What is the height of the tree? (Use \( \sqrt{3} = 1.732 \))

From the top of a building 50 m high, the angle of depression of the base of a tower is 45°. Find the distance between the building and the tower.

A kite is flying at a height of 60 m above the ground. The string attached to the kite makes an angle of 60° with the ground. Find the length of the string.

A man standing on the ground observes the angle of elevation of the top of a tower to be 30°. After walking 50 m towards the tower, the angle of elevation becomes 60°. Find the height of the tower.

The angle of elevation of the top of a building from the foot of a tower is 45°, and the angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the building is 50 m, find the height of the tower.

A ladder 13 m long rests against a wall making an angle of 60° with the ground. Find the height up to which the ladder reaches on the wall.

The shadow of a pole on the ground is 20 m when the angle of elevation of the sun is 30°. Find the height of the pole.

From a point on the ground, the angles of elevation of the top and bottom of a transmission tower are 60° and 30° respectively. If the point is 50 m away from the tower, find the height of the tower.

A man 1.6 m tall is standing at a distance from a tower such that the angle of elevation of the top of the tower is 30°. If the length of the shadow of the man is 2 m, find the height of the tower. (Assume the sun rays are parallel)

Two towers are 30 m apart on level ground. From a point between them, the angles of elevation to the tops of the towers are 60° and 30°. Find the distance of the point from the tower with the greater angle of elevation.