Topic 3.3: Applications of Trigonometry Questions

A box has a square base of side 5 cm. A diagonal of the base has length:

From a point 30 m from a building, the angle of elevation to the top is 54°. What is the height of the building?

A communications antenna is mounted on the roof of a building. The building is 40 m tall and the antenna is 12 m above the roof. From a point P on the ground 60 m from the base, find the angle of elevation to the top of the antenna.

The angle of elevation from point A to the top of a tower is always measured from which direction?

Explain why the angle of elevation from A to B equals the angle of depression from B to A.

A surveyor stands 65 m from the base of a flagpole and measures the angle of elevation to the top to be 28°. Find the height of the flagpole (to 1 d.p.).

A boat is 240 m from the base of a cliff. The angle of elevation from the boat to the top of the cliff is 14°. A seagull sits on top of the cliff. Find the straight-line distance from the boat to the seagull.

A and B stand on level ground. A is 80 m from the base of a tree. The angle of elevation from A to the top of the tree is 22°. Which expression gives the tree's height?

The angle of elevation and the angle of depression between two points are always:

A hot-air balloon is at H, directly above point B on the ground. A woman at A on the ground, with AB horizontal, observes the balloon. The angle of elevation from A to H is 40°. Building height BH = 156 m.

An engineer is planning a ski run. Point A is at the top of the slope at altitude 1800 m; point B is at the base at altitude 1200 m. The horizontal distance from A to B is 750 m.

A lighthouse keeper at height h = 35 m looks down at a ship. The angle of depression is 15°.

Point A is at the base of a vertical cliff. Point B is 50 m from A along flat ground. A rock R is embedded in the cliff face: it is 30 m above A and 10 m horizontally from A (in the direction away from B).
(a) Find the straight-line distance from B to R.
(b) Find the angle of elevation from B to R.

An observer looks down at a boat. The angle of depression is 28°. If the observer is 50 m above the water, what is the horizontal distance to the boat?

A pilot at altitude 2500 m spots an airport ahead. The angle of depression to the runway is 6°.
(a) Find the horizontal distance to the airport.
(b) Find the straight-line distance from the pilot to the airport.

A cuboid has length 4 m, width 3 m and height 2 m. What is the length of the space diagonal (corner to opposite corner)?

In a 3D problem, you are finding the angle a line makes with a horizontal plane. Which step comes FIRST?

A tent has a rectangular base 4 m × 3 m. The vertical pole in the centre is 2 m high. What is the angle the pole makes with a line from the top of the pole to a corner of the base?

When solving a 3D trig problem involving a pyramid, which 2D triangle contains the angle between a slant edge and the base?

A tent has a rectangular base ABCD with AB = 6 m and BC = 4 m. The top T is directly above M, the midpoint of AB. TM = 3 m.
(a) Find the length TC.
(b) Find the angle TC makes with the base.