Question

You are going to use an incline plane to lift a heavy object to the top of a shelving unit with a height of 7 ft. The base of the incline plane is 15 ft from the shelving unit. What is the length of the incline​ plane?
7 ft
15 ft
​(This figure is not drawn to​ scale.)
Question content area bottom
Part 1
The length of the incline plane is about
  
enter your response here ft.
​(Round to the nearest tenth as​ needed.)

Answer 1

To find the length of the incline plane, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the incline plane) is equal to the sum of the squares of the lengths of the other two sides (the height of the shelving unit and the distance from the base of the incline to the shelving unit).

Let:
- \( a = 7 \) ft (height of the shelving unit),
- \( b = 15 \) ft (base distance from the shelving unit).

We need to find the hypotenuse \( c \) (the length of the incline plane).

According to the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]

Substituting the known values:
\[
c = \sqrt{(7)^2 + (15)^2}
\]

Calculating \( (7)^2 \) and \( (15)^2 \):
\[
(7)^2 = 49
\]
\[
(15)^2 = 225
\]

Now, add these values together:
\[
c = \sqrt{49 + 225} = \sqrt{274}
\]

Now, calculate \( \sqrt{274} \):
\[
\sqrt{274} \approx 16.552
\]

Rounding to the nearest tenth:
\[
c \approx 16.6 \text{ ft}
\]

Thus, the length of the incline plane is about **16.6 ft**.