Question

john is using an inclined plane to transport goods from a raised place to the ground. the plane is inclined at an angle of 23° to the horizontal surface. if the goods are at 8 ft height from the ground, what is the length of the inclined plane john is using?
a $\frac{8}{\cos 23}$
b $\frac{8}{\sin 23}$
c $\frac{\cos 23}{8}$
d $\frac{\sin 23}{8}$
e $8\sin 23$

Explanation:

Step1: Recall the sine function in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the height (\(8\) ft) is the side opposite to the angle of \(23^{\circ}\), and the length of the inclined plane (\(l\)) is the hypotenuse.
So, \(\sin23^{\circ}=\frac{8}{l}\)

Step2: Solve for \(l\)

Cross - multiply the equation \(\sin23^{\circ}=\frac{8}{l}\) to get \(l\times\sin23^{\circ}=8\). Then, \(l = \frac{8}{\sin23^{\circ}}\)

Answer:

B. \(\frac{8}{\sin23}\)