Question

A hot air balloon is flying above Grovenburg. To the left side of the balloon, the balloonist measure the angle of depression to the Groveburg soccer fields to be 20 degrees 15’. To the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 62 degrees 30’. The distance between the two athletic complexes is 4 miles.

Answer 1

Find enclosed file with a drawing and the calculations of all angles and all distances.

These are the results that you will find in it:

Angle x = 90° - 22°15’  

Angle y = 90° - 62°30'

Angle z = 22°15’ = 22.25°

Angle w = 62°30’ = 62.50°

 

tan(z) = H/a => a = H/tan(z)

tan(w) = H/b => b = H/tan(w)

 

a+b = 4 => H/tan(z) + H/tan(w) = 4 => H [1/tan(z) + 1/tan(x) ] = 4

    H = 4 / {[1/tan(z) + 1/tan(x) ] } = 1.35 miles

    a = 1.35 / tan(22.25°) =  3.30 miles

    b = 4 – 3.30 = 0.7 miles

I hope it is very useful and you understand it. Let me know.

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