Help on bonus Trig word problem please?

Question

You are traveling toward a mountain at 75 km/hr. You stop at point A and look up to the top of a mountain. The angle of elevation from the ground to the top of the mountain is 0.026 radians. Twenty minutes later, at point B, the angle of elevation is 0.031 radians. About how tall is the mountain? 

I can't figure this out! 
The only think I found out was that the distance from point A to B, which I called distance y, was to be 25 km. I found this using 20mins at 75 km/hr. I drew a picture, but cannot see how it is possible to find the height of the mountain, because it seems to me that there is not enough information, being that they don't give you the time or the distance from point B to the mountain.

Please explain how to do this! Thanks so much.

coreyA · Accepted Answer

Call the distance between the mountain and B, y and the height of the mountain, x. then:

tan(.031) = x/y

and

tan(.026) = x/(25+y)

Now solve for y in the first equation:

y*tan(.031) = x -----> y = x/tan(.031)

Substitute this in for y in the second equation:

tan(.026) = x/(25 + x/tan(.031))

Now solve for x:

(25 + x/tan(.031))tan(.026) = x

25tan(.026) + xtan(.026)/tan(.031) = x

25tan(.026) = x - xtan(.026)/tan(.031)

25tan(.026) = x(1 - tan(.026)/tan(.031))

x = 25tan(.026)/(1 - tan(.026)/tan(.031))

x = 4.0289 km

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Help on bonus Trig word problem please?

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