how do I find the length of the guy wire

Question

find the length of a guy wire that makes an angle of 45 degrees with the ground if the wire is attached to the top of a tower 63 meters high

Answer 1

Draw and label a diagram!

If you must use Trigonometry:

sin 45° = 63 / x

Or you could use the hypotenuse of a 45-45-90 triangle is √2 times a leg.

Answer 2

Dear Cherokee,

If I sketched the wire that forms an 45 degree angle with the ground and attached to the top of 63 meters high tower, I will get a 45-45-90 degree triangle. This helps since this triangle has a special property, so that the distance between the wire to the base of the tower is 63 meters long and the wire itself is 63√2 meters long.

Hope this helps.