Questions: Question 2 10 Points Provide an appropriate response. The rafters of a house make a 30° angle with the joists. If the rafters have a 20-in. overhang and the center of the roof is 12 ft above the joists, how long must the rafters be cut? (A) 24 ft 8 in . (B) 21 ft 8 in . (C) 25 ft 8 in . (D) 26 ft

Question 2
10 Points

Provide an appropriate response.
The rafters of a house make a 30° angle with the joists. If the rafters have a 20-in. overhang and the center of the roof is 12 ft above the joists, how long must the rafters be cut?
(A) 24 ft 8 in .
(B) 21 ft 8 in .
(C) 25 ft 8 in .
(D) 26 ft

Transcript text: Question 2 10 Points Provide an appropriate response. The rafters of a house make a $30^{\circ}$ angle with the joists. If the rafters have a 20 -in. overhang and the center of the roof is 12 ft above the joists, how long must the rafters be cut? (A) 24 ft 8 in . (B) 21 ft 8 in . (C) 25 ft 8 in . (D) 26 ft

Solution

Solution Steps

Step 1: Convert units

Convert the overhang from inches to feet: 20 inches * (1 ft/12 inches) = 5/3 ft. Convert the height from feet to inches: 12 ft * (12 in/1 ft) = 144 in.

Step 2: Calculate the length of the rafter from the joist to the peak.

The height of the roof forms the opposite side of a 30-degree right triangle, and the rafter forms the hypotenuse. We can use the sine function:

sin(30°) = opposite/hypotenuse

sin(30°) = (144 in) / hypotenuse

hypotenuse = 144 in / sin(30°)

hypotenuse = 144 in / (1/2) = 288 in = 24 ft

Step 3: Add the overhang.

Total rafter length = 24 ft + 5/3 ft = 24 ft + 1 ft 8 in = 25 ft 8 in