Question

solve for $x$. round to the nearest tenth, if necessary.
answer attempt 2 out of 2

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
Here, $\theta=26^\circ$, opposite side $=75$, hypotenuse $=x$.

Step2: Substitute values into ratio

$\sin(26^\circ)=\frac{75}{x}$

Step3: Rearrange to solve for $x$

$x=\frac{75}{\sin(26^\circ)}$

Step4: Calculate the value

First, $\sin(26^\circ)\approx0.4384$, so $x\approx\frac{75}{0.4384}\approx171.1$

Answer:

$171.1$