Height and Distance
1. The angle of elevation of the top of a tower is 30° from a point 20 meters away. What is the height of the tower?
A. 10 m
B. 11.55 m
C. 20 m
D. 34.64 m
B. 11.55 m
2. From a 15-meter-high building, the angle of depression to a car is 45°. How far is the car from the building?
A. 7.5 m
B. 15 m
C. 21.21 m
D. 30 m
B. 15 m
3. Two towers of heights 25 m and 35 m stand vertically. If the distance between them is 40 m, what is the distance between their tops?
A. 20√2 m
B. 10√17 m
C. 40 m
D. 50 m
B. 10√17 m
4. A 6-meter-tall pole casts a 2√3-meter-long shadow. What is the sun's angle of elevation?
A. 30°
B. 45°
C. 60°
D. 90°
C. 60°
5. A 10-meter ladder leans against a wall at 60° to the ground. How high does it reach?
A. 5 m
B. 8.66 m
C. 10 m
D. 12 m
B. 8.66 m
6. A person walks 20 m towards a tower. The angle of elevation changes from 30° to 60°. What is the tower's height?
A. 10√3 m
B. 15 m
C. 20 m
D. 30 m
A. 10√3 m
7. From a 45-meter-high cliff, the angle of depression to the far bank of a river is 30°. What is the river's width?
A. 45√3 m
B. 77.94 m
C. 90 m
D. 135 m
B. 77.94 m
8. From a point, the angles of elevation to the top and bottom of a flagstaff are 45° and 30°. If the flagstaff is 10 m tall, how far is the point?
A. 10√3 m
B. 13.66 m
C. 15 m
D. 20 m
B. 13.66 m
9. An airplane is observed at 30° elevation. After flying 1 km vertically, its elevation becomes 60°. What was its initial height?
A. 500 m
B. 750 m
C. 1 km
D. 1.5 km
A. 500 m
10. From 2 km away, the angle of elevation to a mountain's peak is 30°. What is the mountain's height?
A. 1 km
B. 1.15 km
C. 2 km
D. 2.31 km
B. 1.15 km