SOLUTION: 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 6.0 ft from the base of the pole. If the point is 84 ft

Algebra ->  Pythagorean-theorem -> SOLUTION: 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 6.0 ft from the base of the pole. If the point is 84 ft       Log On


   

Question 715001: 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 6.0 ft from the base of the pole. If the point is 84 ft from the base of the cliff, how high is the cliff?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Smaller triangle, 8 ft high and base 6 ft. This fits in the bigger triangle of unknown hight and base 84 feet. The "point" described is part of both of these triangles, and is a shared vertex of these two, similar triangles.
8%2F6=h%2F84, so multiply both side by 84, and h=%284%2F3%2984, 112 feet high cliff.