Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Identify trig - function

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In the right - triangle, $\theta = 46^{\circ}$, the opposite side to the angle is $x$ and the hypotenuse is $16$. So $\sin46^{\circ}=\frac{x}{16}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin46^{\circ}=\frac{x}{16}$ by $16$. We get $x = 16\times\sin46^{\circ}$.
Since $\sin46^{\circ}\approx0.7193$, then $x=16\times0.7193 = 11.5088$.

Step3: Round the answer

Rounding $11.5088$ to the nearest tenth gives $x\approx11.5$.

Answer:

$11.5$