Question

1. solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Use sine function definition

In right - triangle $uvw$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 69^{\circ}$, the hypotenuse is $2.9$ and the side opposite to the angle $\theta$ is $x$. So, $\sin(69^{\circ})=\frac{x}{2.9}$.

Step2: Solve for $x$

Multiply both sides of the equation by $2.9$: $x = 2.9\times\sin(69^{\circ})$.
We know that $\sin(69^{\circ})\approx0.9336$. Then $x = 2.9\times0.9336=2.70744$.

Step3: Round to the nearest tenth

Rounding $2.70744$ to the nearest tenth gives $2.7$.

Answer:

$2.7$