Question

question: 6
jeremy is building a ramp to the entrance of a school. if the ramp needs to vertically rise 6 ft and form an angle of 28° with the ground, which of the following equations should jeremy use to determine the length (x) of the ramp?
a. $\cos 28^{\circ}=\frac{x}{6}$
b. $\cos 28^{\circ}=\frac{6}{x}$
c. $\sin 28^{\circ}=\frac{x}{6}$
d. $\sin 28^{\circ}=\frac{6}{x}$

Explanation:

Step1: Recall the definition of sine function

In a right - triangle, the sine of an angle is defined as the ratio of the opposite side to the hypotenuse.
For the given ramp problem, the vertical rise (opposite side to the angle with the ground) is \(6\) ft and the length of the ramp (\(x\)) is the hypotenuse.
The formula for sine is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)

Step2: Substitute the values into the sine formula

Here, \(\theta = 28^{\circ}\), the opposite side \(= 6\) ft and the hypotenuse \(=x\)
So, \(\sin28^{\circ}=\frac{6}{x}\)

Answer:

D. \(\sin28^{\circ}=\frac{6}{x}\)