A blue print of a shopping complex shows that the bottom edge of the roof to be 93 feet above the ground. If the roof rises to a point 171 feet above the ground over a horizontal distance of 6.5 yards, what is the slope of the roof?
I am positive the answer is twelve, but the book is telling me the answer is 4! Who is right, and if the book is, what did I do wrong?
Mistakes are found in answers in books, but unfortunately not this time.
Watch out: "over a horizontal distance of 6.5 yards,"
Can you take it from here?
To calculate the slope of the roof, we need to determine the change in height (vertical distance) compared to the change in horizontal distance. Given that the bottom edge of the roof is 93 feet above the ground, and it rises to a point 171 feet above the ground over a horizontal distance of 6.5 yards, we can convert the yards into feet for consistency.
First, let's convert 6.5 yards into feet. Since 1 yard is equal to 3 feet, 6.5 yards is equal to:
6.5 yards * 3 feet/yard = 19.5 feet
So, the horizontal distance is 19.5 feet.
Now, let's calculate the change in height (vertical distance):
Change in height = final height - initial height
Change in height = 171 feet - 93 feet
Change in height = 78 feet
To find the slope, we divide the change in height by the horizontal distance:
Slope = change in height / horizontal distance
Slope = 78 feet / 19.5 feet
Calculating this, we find that the slope is:
Slope = 4
Therefore, the book is correct, and the slope of the roof is 4, not 12. It appears that there might have been an error in your calculation or conversion along the way. Double-checking the calculations should help you identify where the mistake occurred.