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 66 ft from the base of the cliff,
How high is the cliff? Round to the nearest unit.
A)2640 ft
B)106 ft
C)528 ft
D)7 ft

Question

Quizplus · Accepted Answer

To solve this problem, we can use 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. The pole and its shadow create a smaller, similar triangle. The ratio of the heights of these triangles will be the same as the ratio of their bases.Let $ h $ be the height of the cliff. The base of the larger triangle (from the base of the cliff to the point where the line meets the ground) is 66 ft, and the height is $ h $. The base of the smaller triangle (the shadow of the pole) is 5 ft, and its height is 8 ft.Using the property of similar triangles, we have:$$ \frac{h}{66} = \frac{8}{5} $$Solving for $ h $:$$ h = \frac{66 \times 8}{5} $$$$ h = \frac{528}{5} $$$$ h = 105.6 $$Rounding to the nearest unit, the height of the cliff is approximately 106 ft.

A Line from the Top of a Cliff to the Ground