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A man at A observes the angle of
elevation of a balloon to be 30 degrees. He then walks 1000
metres towards the balloon to a point B and finds the
elevation to be 60 degrees. If the balloon has height h
metres and the man had x metres left to walk before he is
directly under the balloon show that h=xtan60 and h= (x
+1000) tan30 and use these two equations to find x.

The height of the opposite side of the triangle is the same in both cases and is the height of the balloon.  The angles involved are 30 and 60.  The length of the near side is x+1000 and x.

From this, it is known that when the distance is x and the angle is 60, h/x = tan 60.
It is also known when the distance is x+1000, the angle is 30, so we have h/(x+1000)=tan 30.

Using these two equations, we can solve both for h and get the equations above.
To solve for x, take h = x * tan 60 and put that into the 2nd equation.
This gives (x * tam 60)/(x+1000) = tan 30.

To find x, multiply both sides by x+1000, which gets rid of the fraction.
Subtract x * tan 30 from both sides.
Factor the x term out on the left side.
Divide both sides by the multiple of the x term.

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Scott A Wilson


I have answered every question that was a story problems that had any relation to math for which an answer existed. I have ever answered some questions which had a vague relation to math, but still related.


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