Solve the problem.
-A line from the top of a cliff to the ground passes just over the top of a pole 5.0 ft high and meets the ground at a point 8.0 ft from the base of the pole. If the point is 79 ft from the base of the cliff, how high is the cliff? Round to the nearest unit.
A) 49 ft
B) 3160 ft
C) 395 ft
D) 5 ft

Question

Quizplus · Accepted Answer

The problem can be solved using similar triangles. The triangle formed by the cliff, the ground, and the line from the top of the cliff to the ground is similar to the triangle formed by the pole, the ground, and the line from the top of the pole to the point on the ground. The ratio of the height of the cliff to the height of the pole (5 ft) is the same as the ratio of the distance from the base of the cliff to the point on the ground (79 ft) to the distance from the base of the pole to the point on the ground (8 ft). Thus, the height of the cliff is (79 ft / 8 ft) * 5 ft = 49.375 ft, which rounds to 49 ft.

Solve the Problem. -A Line from the Top of a Cliff to the Cliff