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 determine the length of the ramp, we can use the sine function because we know the height of the truck bed and the angle of the ramp. The relationship involves the opposite side (the height of the truck bed) and the hypotenuse (the length of the ramp).

Using the sine function:
\[
\sin(50^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{42}{\text{ramp length}}
\]

We can rearrange this to find the ramp length:
\[
\text{ramp length} = \frac{42}{\sin(50^\circ)}
\]

Now we calculate \(\sin(50^\circ)\):
\[
\sin(50^\circ) \approx 0.7660
\]

Now we can plug this into our formula to find the ramp length:
\[
\text{ramp length} \approx \frac{42}{0.7660} \approx 54.8 \text{ inches}
\]

Looking at the options provided, it seems like Option #1 is the closest match:
\[
\text{Option #1: } \sin 50°=42x=55 inches
\]

Thus, the length of the ramp is Option #1.