can you solve this word problem for me please?

Question

A wire is stretched from the ground to the top of an antenna tower. the wire is 10 feet long. the height of the tower is 2 ft greater than the distance d from the tower's base to the end of the wire. find the distance d and the height of the tower.

 

the distance from the wire to the shower is what ft

 

the height of the tower is what ft.

Answer 1

you have a right triangle with the hypotenuse 10 feet and the legs d feet and (d+2) feet

this is basically a 3-4-5 right triangle with sides 6, 8, and 10

with a little more practice you'll be able to recognize things like this

that said, here's how to solve the problem algebraically...

10²=d²+(d+2)²

100=d²+d²+4d+4

2d²+4d+4-100=0

2d²+4d-96=0

divide booth sides by 2

d²+2d-48=0

factor

(d+8)(d-6)=0

d-6=0

d=6 feet (distance to the tower)

d+2=6+2=8 feet (height of the tower)