Question

value: 2
solve for x. round to the nearest hundredth if necessary.
24°
x
14

a. 5.69
b. 12.79
c. 6.23
d. 34.42

Explanation:

Step1: Identify the trigonometric ratio

We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 24^{\circ}$, the hypotenuse is 14 and the opposite side to the angle is $x$. So $\sin(24^{\circ})=\frac{x}{14}$.

Step2: Solve for $x$

Multiply both sides of the equation by 14: $x = 14\times\sin(24^{\circ})$.
We know that $\sin(24^{\circ})\approx0.4067$, so $x=14\times0.4067 = 5.6938\approx5.69$.

Answer:

A. 5.69