SOLUTION: Show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth if rounding is needed. a.Find the length of a rect

Algebra ->  Square-cubic-other-roots -> SOLUTION: Show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth if rounding is needed. a.Find the length of a rect      Log On


   

Question 39565: Show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth if rounding is needed.
a.Find the length of a rectangle whose diagonal is 10in. and whose width is 7in.
b. The base of a 15-ft ladder is 5 ft away from a wall. How far above the floor is the top of the ladder?

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
a.Find the length of a rectangle whose diagonal is 10in. and whose width is 7in.
Imagine half of the rectangle as a right triangle: c%5E2+=+a%5E2+%2B+b%5E2
10%5E2+=+7%5E2+%2B+b%5E2
100+=+49+%2B+b%5E2
51+=+b%5E2
sqrt%2851%29+=+b about 7.141 inches
b. The base of a 15-ft ladder is 5 ft away from a wall. How far above the floor is the top of the ladder?
It depends on the location of the floor. I will solve using the idea of the floor's location at the wall. You should imagine this. You see a right triangle forming again.
15%5E2+=+5%5E2+%2B+b%5E2
225+=+25+%2B+b%5E2
200+=+b%5E2
b+=+sqrt%28200%29 about 14.142 feet