Question

which trig function do you use? tangent sine cosine

Explanation:

Step1: Recall trig - function definitions

Sine is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, cosine is $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$, and tangent is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In the right - triangle, we know the hypotenuse (19) and an angle ($40^{\circ}$), and we want to find the side opposite the given angle ($x$).

Step2: Identify the appropriate function

Since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, and we know the hypotenuse and want to find the opposite side with respect to the given angle, we use the sine function.

Answer:

Sine