Question

which ratio would you use to solve for the height of the windmill if given the adjacent?

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, the three main trigonometric ratios are:

• Sine: $\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$
• Cosine: $\cos(A)=\frac{\text{adjacent}}{\text{hypotenuse}}$
• Tangent: $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$

We want to find the height of the windmill (which is the opposite side to angle $A$) and we are given the adjacent side.

Step2: Identify the correct ratio

We know that $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$. If we let the height of the windmill be $h$ (opposite side) and the adjacent side be $a$, then $\tan(A)=\frac{h}{a}$, and we can solve for $h$ as $h = a\times\tan(A)$ when we know angle $A$ and the adjacent side. The sine ratio involves the hypotenuse, and the cosine ratio also involves the hypotenuse, but we don't need the hypotenuse here. So the tangent ratio is the one we should use.

Answer:

TAN (or the tangent ratio, $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$)