Question

A rafter makes an angle of 22.5° with the roof joist, as shown

How tall is the board supporting the middle of the roof?

Answer 1

≈ 5 ft

Explanation:

Using the tangent ratio in the right triangle.

let the height of the board be h , then

tan22.5° =
`(opposite)/(adjacent)` =
`(h)/(12)` ( multiply both sides by 12 )

12 × tan22.5° = h , then

h ≈ 5 ft ( to the nearest whole number )