Question

John views the top of a water tower at an angle of elevation of 36 degrees. He walks 120 meters in a straight line toward the tower. Then he sights the top of the tower at an angle of elevation, 51 degrees. How far is john from the base of the tower?

Answer 1

first draw out a pic

Answer 2

if you focus on the smaller right triangle, you will get

tan(angle) = opp/adj

tan(51) = y/x

x*tan(51) = y

y = x*tan(51)

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If you focus on the largest triangle possible, we see that

tan(36) = y/(x+120)

tan(36) = (x*tan(51))/(x+120) ... plug in y = x*tan(51)

keep going to solve for x to get the final answer