Question

The diagonal braces in a fire tower are 26 ft long

and span a horizontal distance of 24 ft. How high
does each brace reach vertically?
26 ft
24 ft
The height each brace reaches vertically is
(Simplify your answer.)

Answer 1

The height each brace reaches vertically is 10 feet

Explanation:

Let

h -----> the height each brace reaches vertically in feet

d ----> the diagonal braces in feet

x ----> the horizontal distance in feet

Applying the Pythagoras Theorem

`d^2=h^2+x^2`

we have

`d=26\ ft\\x=24\ ft`

substitute

`26^2=h^2+24^2`

Solve for h

`h^2=26^2-24^2`

`h^2=100`

`h=10\ ft`

therefore

The height each brace reaches vertically is 10 feet