# Crane Height

Geometry Level pending

There is a crane and you have measured the spreads between the ground and the top of the crane from two opposing sides as $$\frac{4}{5}$$ and $$\frac{16}{25}$$. These two places from which you measured are a distance of 100 meters apart.

How tall is the crane?

Tip: Use the triple spread formula $$(s_1+s_2+s_3)^2=2(s_1^2+s_2^2+s_3^2)+4s_1s_2s_3$$ and the fact the a spread is equal to the square of the opposite sides length over the hypotenuse side length (reminiscent of $$SOH-CAH-TOA$$).

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