Grade 10 Math — Heights and distances

Use angles of elevation and depression with the standard angles to find a height or a distance you cannot measure directly.

Name: ________________________

1.The Sun is 45° above the horizon. How long a shadow does an upright pole 12 ft tall cast on level ground, in feet?
2.From the top of a cliff 40 ft high, the angle of depression of a boat at sea is 45°. How far is the boat from the base of the cliff, in feet?
3.From the top of a cliff, the angle of depression of a boat is 30°. As the boat sails straight towards the base of the cliff, what happens to the angle of depression?
- a) It increases
- b) It becomes an angle of elevation
- c) It decreases
- d) It stays the same
4.From a window you look down at a car, and from the car someone looks up at the window. How do the angle of depression and the angle of elevation compare?
- a) They add up to 90°
- b) The angle of elevation is larger
- c) They are equal
- d) The angle of depression is larger
5.A kite is flying on a straight string 100 ft long that makes an angle of 30° with the level ground. How high is the kite above the ground, in feet?
6.The angle of elevation of the top of a tower from a point on level ground is 60°, and the point is 45 ft from the base of the tower. Take √3 = 1.73. How tall is the tower, in feet?
7.An upright pole casts a shadow. Put these angles of elevation of the Sun in order, shortest shadow first.
- 60°
- 75°
- 30°
- 45°
8.A tree is 20 ft tall. From a point on level ground the angle of elevation of its top is 30°. Take √3 = 1.73. How far is that point from the base of the tree, in feet?

Answer key — Grade 10 Math — Heights and distances