Find Length of Guy Wire

[greatwhiteshark]

A radio transmission tower is 200 feet high. How long should a guy wire be if it is to be attached to the tower 10 feet from the top and is to make an angle of 21 degrees with the ground.

This is my work:

tan 21 degrees = 200 feet/y

y = 200 feet/tan21 degrees

y = 521.02 feet

I then used the Pythagorean Theorem and found x to equal 558.09 feet for the guy wire. However the book's answer is 555 feet.

My question:

How do I find 555 feet?

 

[tkhunny]

10 feet from the top

You missed that part. Use 190, not 200.

 

[greatwhiteshark]

Hey

I used 190 feet but was not able to find 555 feet as the length of guy wire.

 

[tkhunny]

Don't give up. Keep plugging until you KNOW the answer.

Using 200 ft, which is wrong, I get 558.086 ft.
Using 190 ft, which is correct, I get 530.181 ft.

Here's the fun part,

If I start with 190 ft, but forget, and use 200 ft in the Pythagorean Theorem, I get 533.847 ft. OK, that's pretty meaningless.

If I start with 200 ft, but forget, and use 190 ft in the Pythagorean Theorem, I get 554.581 ft. OK, that's pretty suspicious, given the book's answer.

 

[greatwhiteshark]

okay

I understand what you mean. I can now solve similar questions.