Topic 3.3: Applications of Trigonometry Questions

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

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:

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

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.

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.

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

A flagpole stands at the corner of a rectangular park. The park is 50 m × 35 m. The pole is 20 m tall.

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 mountain peak at height 2450 m is observed from a weather station at height 850 m. The horizontal distance between them is 3.2 km. Find the angle of elevation from the station to the peak.

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 statue stands on top of a pedestal. From a point 20 m away on level ground, the angle of elevation to the top of the statue is 55°, and to the top of the pedestal is 40°. Find the height of the statue.

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

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 ship P is 20 km due north of port O. Ship Q is 15 km due east of O. Both ships are at sea level. A helicopter at H is 3 km directly above O.

A vertical pole stands at one corner O of a rectangular field. The field is OABC, where OA = 8 m and OC = 6 m. The top of the pole is T, with OT = 5 m. (a) Find the distance OB (diagonal of the field). (b) Find the angle the line TB makes with the horizontal.

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?