Question

The roads that connect three buildings form a right triangle. Use the image to find the distance between the parking garage and the theater.

Answer 1

c=100yd, a=60yd, find b
(60yd)^2+b^2=(100yd)^2
3600 yd^2+ b^2 = 10000 yd^2
b^2 = 10000-3600 yd^2
b = sqrt(6400 yd^2)
b=80 yd

Answer 2

`80\ yd`

Explanation:

Let

x------> the distance between the parking garage and the theater

we know that

In a right triangle

Applying the Pythagoras Theorem

`c^(2) =a^(2)+b^(2)`

where

c is the hypotenuse

a,b are the legs of the triangle

In this problem we have

`c=100\ yd, a=60\ yd, b=x\ yd`

substitute and solve for x

`100^(2) =60^(2)+x^(2)`

`x^(2)=100^(2)-60^(2)`

`x^(2)=6,400`

`x=80\ yd`