Question

the picture below shows a box sliding down a ramp: what is the distance, in feet, that the box has to travel to move from point a to point c? 10 cos 62° 10 sin 62°

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 62^{\circ}\), the opposite side is \(AB = 10\) (given), and the hypotenuse is \(AC\) (the distance we want to find). So, \(\sin62^{\circ}=\frac{AB}{AC}\).

Step2: Solve for \(AC\)

From \(\sin62^{\circ}=\frac{10}{AC}\), we can cross - multiply to get \(AC\times\sin62^{\circ}=10\), then \(AC = \frac{10}{\sin62^{\circ}}\).

Answer:

\(\frac{10}{\sin62^{\circ}}\)