Two wires a 50 ft apart tether a balloon to the ground as s

Two wires, a = 50 ft apart, tether a balloon to the ground, as shown. How high is the balloon above the ground?

Solution

tan75 = h/(50+x)
and
tan85 = h/x

Now set both equal to h

(50+x)tan75 = h
xtan85 = h

solve for x

xtan85 = 50tan75+xtan75

xtan85 - xtan75 = 50tan75

x(tan85-tan75) = 50tan75

x = (50tan75) / (tan85-tan75)

x = 24.24

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tan85 = h/x

xtan85 = h

h = 277 feet