Question

using trig to find a side
score: 0/2 penalty: none
question
solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of 2

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine function is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 19^{\circ}$, the hypotenuse $US = 9.9$, and the opposite side to the angle $19^{\circ}$ is $UT=x$.

Step2: Apply the sine formula

We have $\sin(19^{\circ})=\frac{x}{9.9}$.

Step3: Solve for \(x\)

Multiply both sides of the equation by \(9.9\): \(x = 9.9\times\sin(19^{\circ})\).
Since $\sin(19^{\circ})\approx0.3256$, then \(x=9.9\times0.3256 = 3.22344\).

Answer:

\(3.2\)