Question

given right triangle jkl, what is the value of cos(l)?

Explanation:

Step1: Recall cosine formula

The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For angle $L$ in right - triangle $JKL$, the side adjacent to angle $L$ is $KL = 5$ and we first need to find the hypotenuse $JL$.

Step2: Use Pythagorean theorem

By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 5$, $b = 12$, and $c$ is the hypotenuse. So $JL=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13$.

Step3: Calculate cosine of angle $L$

$\cos(L)=\frac{KL}{JL}$. Since $KL = 5$ and $JL=13$, then $\cos(L)=\frac{5}{13}$.

Answer:

$\frac{5}{13}$