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Homework Statement
In traveling across flat land, you notice a mountain peak directly in front of you. Its angle of elevation (to the peak) is 3.5 degrees. After you drive 13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.
Homework Equations
The Attempt at a Solution
I drew out the triangle, and I'm figuring that the adjacent side can be called 13+x. So, I tried using a tangent function to find the length of x, and find the overall length of the adjacent side. Theta measurements are in degrees.
[tex] tan \ 3.5 = \frac{sin \ 3.5}{13 + x}[/tex]
Then I solved for x:
[tex] sin \ 3.5 = 13 + x \ tan \ 3.5[/tex]
[tex] x = \frac{sin \ 3.5}{tan \ 3.5} - 13 [/tex]
[tex] x = approximately -12 \ miles [/tex]
Clearly, -12 miles is not the correct answer for the value of the remaining distance in the adjacent side.
If I take the positive value of 12 though, and make the adjacent side 25 altogether, the answer seems to come out as something that's potentially feasible...
[tex]tan \ 3.5 = \frac{opp}{25}[/tex]
[tex] 25 \ tan \ 3.5 = opp[/tex]
Then I get opp = approximately 1.5 miles, or 7920 feet in height.
I'm thinking I did something wrong with the initial equation to find x though. I'm thinking the 9 degree angle of elevation needs to be figured in...but how? We haven't covered any problems even remotely like this in class, I'm just working through the more challenging problems that the professor seems to not want to assign as homework. Any suggestions would be much appreciated!
edit- I just realized that I should have subtracted the 13 over to the other side before dividing, but that still doesn't solve the problem in either case.