SOLUTION: A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is A = 65°. He then walks s = 130 feet further away and observes that th

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Question 1149535: A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is A = 65°. He then walks s = 130 feet further away and observes that the angle of elevation to the top of the antenna is B = 48°
Find the height of the antenna to the nearest foot
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We have to assume, of course, that the land is flat around the tower where the man is walking, so that we are working with right triangles....

If the distance from the man to the tower on the first observation is x, then the distance from the second observation is x+130.

Then if y is the height of the antenna, we have two equations relating the height of the tower, the two distances, and the appropriate trig function:

tan%2865%29+=+y%2Fx
tan%2848%29+=+y%2F%28x%2B130%29

One straightforward way to solve the problem with pencil-and-paper mathematics from there is to eliminate y to solve for x and then find the height of the tower by using that value of x in either equation.

y+=+x%2Atan%2865%29
y+=+%28x%2B130%29%2Atan%2848%29

x%2Atan%2865%29+=+%28x%2B130%29%2Atan%2848%29

I'll let you finish from there.

If an algebraic solution is not required, the fastest path to the answer is to graph the two equations x%2Atan%2865%29 and %28x%2B130%29%2Atan%2848%29 on a graphing calculator and find where they intersect; that will immediately give you the values of both x and y.