document.write( "Question 1196967: One mountain peak is 10 miles due east of another. A hiker locates the first mountain peak at an angle of 65° W of N, and the second at an angle of 32° N of E. How far is the hiker from each mountain peak? \n" ); document.write( "
Algebra.Com's Answer #830100 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
i believe i have it.
\n" ); document.write( "distance from the hiker to the first mountain peak is equal to 6.318562788 miles.
\n" ); document.write( "distance from the hiker to the second mountain peak is equal to 5.039145022 miles.
\n" ); document.write( "here's my diagram that i drew for this problem.
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\n" ); document.write( "the basic idea was to find the value of y first.
\n" ); document.write( "i started with tan(25) = y/x and tan(32) = y/(10-x)
\n" ); document.write( "from that i solved for y to get:
\n" ); document.write( "y = x * tan(25) and y = (10-x) * tan(32)
\n" ); document.write( "since y = y, then x * tan(25) = (10-x) * tan(32)
\n" ); document.write( "from that, i solved for x to get x = 5.726562658.
\n" ); document.write( "from that, i solved for (10-x) to get (10-x) = 4.273437342.
\n" ); document.write( "i used the values for x and 10-x to solve for y.
\n" ); document.write( "i used tan(25) = y/x and tan(32) = y/(10-x)
\n" ); document.write( "i solved for y to get y = 2.670340022.
\n" ); document.write( "i used the value of y to get the value of W and the value of z.
\n" ); document.write( "i used sin(25) = y/w and sin(32) = y/z
\n" ); document.write( "i got the value of w = 6.318562788.
\n" ); document.write( "i got the value of z = 5.039145022.
\n" ); document.write( "w was the distance from the hiker at C to the first mountain peak at A.
\n" ); document.write( "z was the distance from the hiker at C to the second mountain peak at B.
\n" ); document.write( "i used pythagorean theorem to make sure the values in triangle AFC and FBC were good.
\n" ); document.write( "they looked good.
\n" ); document.write( "your solution is, to the best of my knowledge:
\n" ); document.write( "distance from the hiker to the first mountain peak is equal to 6.318562788 miles.
\n" ); document.write( "distance from the hiker to the second mountain peak is equal to 5.039145022 miles.\r
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