Question

Bob is told that the pitch on the roof of his garage is 5-12, meaning that for every 5 feet the roof increases vertically, it increases 12 feet horizontally. if θ is defined as the angle at the corner of the roof formed by the pitch of the roof and a horizontal line, what is sinθ?

Answer 1

`sin(\theta)=(5)/(13)`

Explanation:

step 1

Find the hypotenuse of the right triangle with legs of 5 ft and 12 ft

Applying the Pythagoras Theorem

Let

d ----> the length of the hypotenuse

`d^(2)=12^2+5^2`

`d^(2)=169`

`d=13\ ft`

step 2

Find the sine of angle theta

Remember that

The sine of angle theta is equal to divide the opposite side of angle theta (5 feet) by the hypotenuse (13 feet)

`sin(\theta)=(5)/(13)`