Final answer:
To find the rafter length when the rise is 8 ft and the angle is 35.5 degrees, use the sine function to calculate that the rafter length is approximately 13.78 ft, which when rounded to the tenths place based on the given degree is 13.8 ft.
Step-by-step explanation:
To calculate the length of the rafter required for a roof when the rafter makes an angle of 35.5 degrees with the joist and the rise is 8 ft, we can use trigonometric functions, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (rise) to the adjacent side (run). Since we have the angle and the opposite side, we can find the hypotenuse (rafter length) using the tangent function.
We know that tan(35.5°) = rise/run and the rise is given as 8 ft. Rearranging this, run = rise / tan(35.5°). However, to find the length of the rafter, which is the hypotenuse, we should use the sine function, as sin(35.5°) = rise/rafter. Solving for the rafter gives us rafter = rise / sin(35.5°).
Let's calculate it:
- First, convert the angle to radians if your calculator is set to radian mode.
- Next, calculate the sine of 35.5 degrees, which is approximately 0.5807.
- Finally, calculate the rafter length by dividing the rise (8 ft) by the sine of 35.5 degrees.
Rafter length = 8 ft / sin(35.5°) ≈ 8 ft / 0.5807 ≈ 13.78 ft.
However, you asked for the answer to be rounded to the tenths place based on 35.5 degrees. Therefore, we should round 13.78 to the closest tenth, which would be 13.8 ft as the final answer after applying rounding.