Question

1. which trig ratio would you use to solve for the missing side?

a) sine
b) cosine
c) tangent

Explanation:

Step1: Recall trig - ratio definitions

Sine is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, cosine is $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and tangent is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Analyze the given triangle

We know one non - right angle ($40^{\circ}$) and we want to find a side. If we assume the known side is adjacent to the $40^{\circ}$ angle and we want to find the opposite side to the $40^{\circ}$ angle, we use the tangent ratio since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Answer:

c) Tangent