SOLUTION: Was told I used Tan incorrectly.. During a windstorm, part of the top of a flagpole breaks off. The broken top portion touches the ground at an angle of 75° 12 feet from its base.

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Question 946528: Was told I used Tan incorrectly..
During a windstorm, part of the top of a flagpole breaks off. The broken top portion touches the ground at an angle of 75° 12 feet from its base.
How tall was the pole before the windstorm?
Round your answer to one decimal place and show steps.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!

You want to be able to find the sum of the remaining vertical piece and the hypotenuse piece.

x=12
y, unknown
h, unknown hypotenuse

tan%2875%29=y%2F12
y=12%2Atan%2875%29

Realize, the parts of x, y, and h form a right-triangle and you can find h using Pythagorean Theorem.

x%5E2%2By%5E2=h%5E2
h=sqrt%28x%5E2%2By%5E2%29
h=sqrt%28144%2B144%2A%28tan%2875%29%29%5E2%29

Now, you want to know the sum of y and h, the full length of the flag pole before it broke.

12%2Atan%2875%29%2Bsqrt%28144%2B144%2A%28tan%2875%29%29%5E2%29
and should simplify,
highlight%2812%2Atan%2875%29%2B12%2Asqrt%281%2B%28tan%2875%29%29%5E2%29%29

Approximation for the tan function of 75 degrees,
tan(75)=3.7320