Applications of trigonometry hard

Applications of Trigonometry Quiz (Hard)

1. An observer is standing at point A. She notices two birds in the sky. The angle of elevation of bird 1 is 75°, and the angle of elevation of bird 2 is 45°. If bird 1 is vertically above bird 2, what is the angle between the lines of sight from point A to bird 1 and bird 2?

a) 30° b) 60° c) 90°

2. From the top of a tower 100 meters high, the angle of depression of a point on the ground is 60°. What is the distance between the top of the tower and the point on the ground?

a) 50 meters b) 100 meters c) 100√3 meters

3. An observer on the ground is watching a kite flying in the sky. The angle of elevation of the kite is 30°. If the kite's string is 200 meters long, how high is the kite from the ground?

a) 100 meters b) 200 meters c) 200√3 meters

4. The angle of elevation of the top of a tower from a point on the ground is 45°. If the height of the tower is 50 meters, what is the distance between the point on the ground and the base of the tower?

a) 50 meters b) 50√3 meters c) 25 meters

5. A ladder is leaning against a wall. The ladder makes an angle of 75° with the ground, and its foot is 4 meters away from the wall. How high does the ladder reach on the wall?

a) 1 meter b) 3 meters c) 4 meters

6. The angle of elevation of a helicopter from a point on the ground is 60°. The helicopter then moves 300 meters horizontally and ascends vertically by 150 meters. What is the new angle of elevation of the helicopter from the same point?

a) 30° b) 45° c) 60°

7. An observer is 60 meters away from a building. The angle of elevation of the top of the building is 30°. If the observer moves towards the building by 20 meters, what will be the new angle of elevation of the top of the building?

a) 45° b) 60° c) 75°

8. A staircase is built such that each step is 25 cm high. If the height of the staircase is 2.5 meters, how many steps are there in the staircase?

a) 10 steps b) 12 steps c) 15 steps

9. The angle of depression of a boat from the top of a lighthouse is 30°. After moving 100 meters horizontally towards the lighthouse, the angle of depression becomes 45°. What is the height of the lighthouse?

a) 100 meters b) 150 meters c) 200 meters

10. The angle of elevation of the top of a flagpole from a point on the ground is 60°. If the flagpole is 5 meters high, what is the distance between the point on the ground and the base of the flagpole?

a) 5 meters b) 5√3 meters c) 10 meters