How tall is the pole?

Question

Two wires stretch from a pole to two points on the ground which are 100 feet apart. The first wire is to the left of the pole and forms a 30 degree angle with the ground. The second wire is to the right of the pole and forms a 60 degree angle with the ground. How tall is the pole? Simplify your answer.

Answer 1

Draw and label diagram!

h represents the height of the pole

x represents the distance from pole to point to the left

100 - x represents the distance from the pole to the point to the right.

h / x = tan 30°

h = x tan 30°

h / tan 30° = x

h / (100 - x) = tan 60°

h = (100 - x) tan 60°h

h = 100 tan 60° - x tan 60°

h - 100 tan 60° = - x tan 60°

(h - 100 tan 60°) / -tan 60° = x

h / tan 30° = (h - 100 tan 60°) / -tan 60°

Can you solve for h and answer?