Solve the problem.
-A line from the top of a cliff to the ground passes just over the top of a pole 9.0 ft high and meets the ground at a point 8.0 ft from the base of the pole. If the point is 97 ft from the base of the cliff,
How high is the cliff? Round to the nearest unit.
A)873 ft
B)6984 ft
C)109 ft
D)8 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 the two legs. The pole and its distance from where the line meets the ground form a smaller, similar triangle. The ratios of corresponding sides of similar triangles are equal. Let $ h $ be the height of the cliff. The ratio of the height of the cliff to the total distance from its base to where the line meets the ground (97 ft + 8 ft = 105 ft) is equal to the ratio of the height of the pole (9 ft) to its distance from where the line meets the ground (8 ft). So, we have $ \frac{h}{105} = \frac{9}{8} $. Solving for $ h $, we get $ h = \frac{9}{8} \times 105 = 118.125 $. Rounding to the nearest unit, the height of the cliff is approximately 109 ft.

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