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From a balloon.......

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1 Answer

You can draw a right triangle with the first point (A) as the balloon, the second point (B) the HQ, and the third point (C) directly above HQ, to the side of the balloon. 
 
The angle BAC is 70°31'.  This is (70+31/60)° ≈ 70.5167°
Side BC is 734.
The hypotenuse AB is unknown.  We will call it x.
 
Side BC is opposite the angle.  We know that:
sinθ=opposite/hypotenuse
 
So we can say:
sin(70.5167)=734/x
x*sin(70.5167)=734          (multiply both sides by x)
x=734/(sin(70.5167))        (divide both sides by sin(70.5167)
Put in into the calculator for 778.5826≈ 779 ft