Final answer:
By applying the Pythagorean theorem, which states that in a right-angled triangle the square of the hypotenuse is the sum of the squares of the other two sides, it was determined that the height of the ridge is 9 feet.
Step-by-step explanation:
The student is trying to find the height of the ridge of a rafter based on the given slope and run. To solve this, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, the slope of the rafter is the hypotenuse (15 feet), and half of the run is one of the legs of the triangle (12 feet). The task is to find the height of the ridge, which is the other leg of the triangle.
According to the Pythagorean theorem:
height of the ridge² + (half the run)² = (slope of the rafter)²
height of the ridge² + 12² = 15²
height of the ridge² + 144 = 225
height of the ridge² = 225 - 144
height of the ridge² = 81
Now take the square root of both sides:
height of the ridge = √81
height of the ridge = 9 feet
Hence, the correct answer is option (a) 9 feet.