Question

Fatima and Tia are loading a refrigerator into the back of a truck. They know they need the ramp to make a 50-degree angle with the ground to reach the truck bed, which is 42 inches from the ground. How long is the ramp?

Option #1: sin 50°=42x=55 inches

Option #2: cos 50°=42x=48 inches

Option #3: sin 42°=x42=63 inches

Option #4: cos 42°=42x=62 inches

(1 point)
The length of the ramp is Option #

Answer 1

To find the length of the ramp, we can use the sine function, which relates the angle of the ramp, the height of the refrigerator, and the length of the ramp.

Given:
- Height (opposite side) = 42 inches
- Angle (θ) = 50 degrees

Using the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
\[
\sin(50°) = \frac{42}{x}
\]

Where \( x \) is the length of the ramp (hypotenuse). We can rearrange this to solve for \( x \):
\[
x = \frac{42}{\sin(50°)}
\]

Now, calculate the sine of 50 degrees:
\[
\sin(50°) \approx 0.766
\]

Then, substituting this value back in:
\[
x = \frac{42}{0.766} \approx 54.8 \text{ inches}
\]

Rounding this gives approximately 55 inches.

So, the length of the ramp is closest to **Option #1: sin 50°=42x=55 inches**.