Question

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

Explanation:

Step1: Find the hypotenuse

By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 5\), \(b=12\). So \(c=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13\).

Step2: Recall cosine - ratio definition

The cosine of an angle in a right - triangle is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle L\), the adjacent side to \(\angle L\) is \(KL = 5\) and the hypotenuse is \(JL=13\). So \(\cos(L)=\frac{5}{13}\).

Answer:

A. \(\frac{5}{13}\)