Question

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

Explanation:

Step1: Identify trigonometric relation

In right - triangle $LMN$ with $\angle L = 39^{\circ}$ and opposite side $MN = 40$ and hypotenuse $LN=x$. We use the sine function $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(39^{\circ})=\frac{40}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\times\sin(39^{\circ}) = 40$. Then $x=\frac{40}{\sin(39^{\circ})}$.

Step3: Calculate the value

We know that $\sin(39^{\circ})\approx0.6293$. So, $x=\frac{40}{0.6293}\approx63.6$.

Answer:

$63.6$