Question

question 12(multiple choice worth 4 points)
(05 04 lc)
the sail of a boat is in the shape of a right triangle. which expression shows the height, in meters, of the sail?
8/tan35°
8/cos35°
8(tan35°)
8(cos35°)

Explanation:

Step1: Recall trigonometric ratio

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the height of the sail be $h$. Here, $\theta = 35^{\circ}$, the adjacent side to the angle $35^{\circ}$ is $h$ and the opposite side is $8$.
So, $\tan35^{\circ}=\frac{8}{h}$.

Step2: Solve for $h$

Cross - multiply the equation $\tan35^{\circ}=\frac{8}{h}$ to get $h\times\tan35^{\circ}=8$. Then, $h = \frac{8}{\tan35^{\circ}}$.

Answer:

$\frac{8}{\tan35^{\circ}}$ (the second option)