Question

in △jkl, solve for x.

Explanation:

Step1: Identify trigonometric relation

In right - triangle $\triangle{JKL}$, we know the adjacent side to angle $L = 34$ and we want to find the hypotenuse $x$. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 27^{\circ}$, adjacent side to $\angle{L}$ is $KL = 34$ and hypotenuse is $x$. So, $\cos(27^{\circ})=\frac{34}{x}$.

Step2: Solve for $x$

We can re - arrange the equation $\cos(27^{\circ})=\frac{34}{x}$ to $x=\frac{34}{\cos(27^{\circ})}$. Since $\cos(27^{\circ})\approx0.891$, then $x=\frac{34}{0.891}\approx38.16$.

Answer:

38.16