To find the length of the ramp, we can use trigonometric functions based on the given angle and height of the truck bed. Here, we use the sine function because we have the opposite side (the height of the truck bed) and we want to find the hypotenuse (the length of the ramp).
Step 1: Use the sine function
The relationship between the angles and the sides in a right triangle can be expressed with the sine function: \[ \sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}} \] In this case:
- The angle is 50 degrees.
- The opposite side is the height of the truck bed (42 inches).
- The hypotenuse is the length of the ramp (let's call it \( x \)).
Step 2: Set up the equation
\[ \sin(50^\circ) = \frac{42}{x} \]
Step 3: Solve for \( x \)
Rearranging the equation gives us: \[ x = \frac{42}{\sin(50^\circ)} \]
Step 4: Calculate the value
Now we need to calculate \( \sin(50^\circ) \) using a calculator: \[ \sin(50^\circ) \approx 0.766 \] Using this value: \[ x = \frac{42}{0.766} \approx 54.8 \text{ inches} \]
Conclusion
The closest answer to the calculated length of the ramp would be approximately 55 inches, which corresponds to:
Option #1: sin 50°=42/x=55 inches.
This option is correct.
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