SOLUTION: A guy wire makes a 65° angle with the ground. Walking out 37 feet further from the tower, the angle of elevation to the top of the tower is 39°. Find the height of the tower.

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Question 1089628: A guy wire makes a 65° angle with the ground. Walking out 37 feet further from the tower, the angle of elevation to the top of the tower is 39°. Find the height of the tower.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Guy wire at ground is x feet; tower is y feet.

system%28tan%2865%29=y%2Fx%2Ctan%2839%29=y%2F%28x%2B37%29%29


y=%2837tan%2839%29%2Atan%2865%29%29%2F%28tan%2865%29-tan%2839%29%29


%2837%2A0.80978%2A2.1445%29%2F%282.1556-0.0978%29

64.253%2F1.3347

highlight%28y=48%2Afeet%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A guy wire makes a 65° angle with the ground. Walking out 37 feet further from the tower, the angle of elevation to the top of the tower is 39°. Find the height of the tower.
Use law of sines, along with the 39o, and 26o ∡ (65 - 39), and the 37' to get the length of the guy wire.

With the length of the guy wire, use sine ratio: matrix%281%2C4%2C+%22sin%22%2C+65%5Eo%2C+%22=%22%2C+O%2FH%29, along with the 65o to get the height of the tower.

You should get a height of: highlight_green%28matrix%281%2C2%2C+48.14013212%2C+feet%29%29

IGNORE, IGNORE, IGNORE the person who gave you a RIDICULOUS answer, unless of course you want to get the WRONG answer!