Question

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

5/13
5/12
12/13
12/5

Explanation:

Step1: Find the length of the hypotenuse \(JL\)

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

Step2: Use the cosine 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 \(JL=13\).
So \(\cos(L)=\frac{KL}{JL}=\frac{5}{13}\).

Answer:

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