Math CentralQuandaries & Queries


Question from C, a teacher:

Chelcy and Jorgeare 2.32 miles apart. The observe a hot air balloon directly overhead between them Chelcy's angle of elevation is 28 degrees. Jorge's Angle of elevation is 37 degrees. What is the altitude of the balloon?


I drew a diagram. (Not to scale.)


Chelcy is at C, Jorgeare is at J, P is the point between them directly below the balloon B and h is the height of the balloon in miles. Suppose the distance from J to P is x miles. What is he distance from P to C?

$\tan( 37^o) = \frac{h}{x}.$ What is $\tan(28^o)?$ Solve the first equation for $x$ and substitute into the second equation. Solve for $h.$


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