Applications of trigonometry medium

Applications of Trigonometry Quiz (Medium)

1. A building casts a shadow of 15 meters when the angle of elevation of the sun is 45°. What is the height of the building?

a) 15 meters b) 30 meters c) 10 meters

2. In a right-angled triangle, if one acute angle is 35°, what is the measure of the other acute angle?

a) 55° b) 45° c) 35°

3. The angle of elevation of an airplane from a point on the ground is 30°. If the airplane is flying at an altitude of 600 meters, how far is it from the point on the ground?

a) 300 meters b) 600 meters c) 300√3 meters

4. The angle of elevation of the top of a tower from two points at a distance of 30 meters and 60 meters from the base of the tower are 30° and 45°, respectively. What is the height of the tower?

a) 20 meters b) 30 meters c) 40 meters

5. An observer on the ground is watching a kite flying in the sky. The angle of elevation of the kite is 60°. If the kite's string is 100 meters long, how high is the kite from the ground?

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

6. The angle of depression of a boat from the top of a lighthouse is 45°. If the height of the lighthouse is 30 meters, how far is the boat from the lighthouse?

a) 30 meters b) 30√3 meters c) 15 meters

7. The angle of elevation of a hot air balloon from a point on the ground is 60°. After ascending vertically for 100 meters, the angle of elevation becomes 30°. What is the initial height of the balloon from the ground?

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

8. The angle of elevation of the top of a tower from a point on the ground is 60°. If the tower is 40 meters high, how far is the point from the base of the tower?

a) 20 meters b) 20√3 meters c) 40 meters

9. The angle of elevation of the top of a tree from a point on the ground is 45°. If the tree is 10 meters tall, how far is the point from the tree?

a) 10 meters b) 10√2 meters c) 20 meters

10. The angle of elevation of a mountain peak from a point on the ground is 30°. After walking 100 meters towards the mountain, the angle of elevation becomes 45°. What is the height of the mountain?

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