SOLUTION: 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 hik
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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?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe i have it.
distance from the hiker to the first mountain peak is equal to 6.318562788 miles.
distance from the hiker to the second mountain peak is equal to 5.039145022 miles.
here's my diagram that i drew for this problem.
the basic idea was to find the value of y first.
i started with tan(25) = y/x and tan(32) = y/(10-x)
from that i solved for y to get:
y = x * tan(25) and y = (10-x) * tan(32)
since y = y, then x * tan(25) = (10-x) * tan(32)
from that, i solved for x to get x = 5.726562658.
from that, i solved for (10-x) to get (10-x) = 4.273437342.
i used the values for x and 10-x to solve for y.
i used tan(25) = y/x and tan(32) = y/(10-x)
i solved for y to get y = 2.670340022.
i used the value of y to get the value of W and the value of z.
i used sin(25) = y/w and sin(32) = y/z
i got the value of w = 6.318562788.
i got the value of z = 5.039145022.
w was the distance from the hiker at C to the first mountain peak at A.
z was the distance from the hiker at C to the second mountain peak at B.
i used pythagorean theorem to make sure the values in triangle AFC and FBC were good.
they looked good.
your solution is, to the best of my knowledge:
distance from the hiker to the first mountain peak is equal to 6.318562788 miles.
distance from the hiker to the second mountain peak is equal to 5.039145022 miles.
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