Solve the problem.
-A line from the top of a cliff to the ground passes just over the top of a pole 8.0 ft high and meets The ground at a point 5.0 ft from the base of the pole. If the point is 99 ft from the base of the cliff, How high is the cliff? Round to the nearest unit.
A) 3960 ft
B) 8 ft
C) 792 ft
D) 158 ft

Question

Quizplus · Accepted Answer

The problem can be solved using similar triangles. The line from the top of the cliff to the ground creates a right triangle with the ground and the height of the cliff as its sides. The pole and its distance from the point where the line meets the ground create a smaller, similar triangle. The ratio of the height of the cliff to the total distance from its base to the point where the line meets the ground (99 ft + 5 ft = 104 ft) is the same as the ratio of the height of the pole (8 ft) to its distance from the point where the line meets the ground (5 ft). Therefore, the height of the cliff is to 104 ft as 8 ft is to 5 ft. Solving for the height of the cliff (h) gives us h/104 = 8/5, so h = (8/5) * 104 = 166.4 ft, which rounds to 158 ft to the nearest unit.

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