Applications of Trigonometry

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. The height of the tower is:

If the height of a tower and the distance of the point of observation from its foot are both increased by 10%, then the angle of elevation of its top:

The angle of elevation of the sun when the shadow of a pole $h$ meters high is $\sqrt{3}h$ meters long is:

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is:

The angle of depression of a car parked on the ground from the top of a 75 m high tower is 30°. The distance of the car from the base of the tower is:

If the length of the shadow of a tower is decreasing, then the angle of elevation of the sun is:

A tower is 50 m high. What is the angle of elevation of its top from a point 50 m away from its foot on the ground?

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

The ratio of the height of a tower and the length of its shadow on the ground is $\sqrt{3} : 1$. What is the angle of elevation of the sun?

If a pole 6 m high casts a shadow 2√3 m long on the ground, then the sun's elevation is:

The line drawn from the eye of an observer to the point in the object viewed by the observer is called:

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is:

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45°. The height of the tower is:

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is 30°.

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top from the same point will be:

When the altitude of the sun is 45°, the length of the shadow of a tower is equal to:

The angle of depression of an object from a point 100 m high above the ground is 60°. The distance of the object from the base of the point is:

The angle of elevation of the sun is $60^{\circ}$, then the length of the shadow of a $15\text{ m}$ high tree is:

If the height of a pole and the length of its shadow on the ground are equal, then the angle of elevation of the sun is:

The shadow of a tower is $\sqrt{3}$ times its height. The angle of elevation of the sun is:

The angle of elevation of the top of a tower from a point on the ground is 30°. If the height of the tower is 20√3 metres, then the distance of the point from the base of the tower is: