Question 1149535
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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....<br>
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.<br>
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:<br>
{{{tan(65) = y/x}}}
{{{tan(48) = y/(x+130)}}}<br>
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.<br>
{{{y = x*tan(65)}}}
{{{y = (x+130)*tan(48)}}}<br>
{{{x*tan(65) = (x+130)*tan(48)}}}<br>
I'll let you finish from there.<br>
If an algebraic solution is not required, the fastest path to the answer is to graph the two equations {{{x*tan(65)}}} and {{{(x+130)*tan(48)}}} on a graphing calculator and find where they intersect; that will immediately give you the values of both x and y.<br>