Question

express cos j as a fraction in simplest terms.
(right triangle with right angle at k, lk=10, lj=26)
answer attempt 1 out of 3
cos j = blank submit answer

Explanation:

Step1: Identify the sides for cosine

In right triangle \( \triangle JKL \) with right angle at \( K \), for angle \( J \), cosine is adjacent over hypotenuse. First, find the length of the adjacent side to \( J \). We know \( LK = 10 \), \( LJ = 26 \). Use Pythagorean theorem to find \( JK \): \( JK=\sqrt{LJ^{2}-LK^{2}}=\sqrt{26^{2}-10^{2}}=\sqrt{676 - 100}=\sqrt{576} = 24 \).

Step2: Calculate \( \cos J \)

Adjacent side to \( J \) is \( JK = 24 \), hypotenuse is \( LJ = 26 \). So \( \cos J=\frac{JK}{LJ}=\frac{24}{26}=\frac{12}{13} \).

Answer:

\(\frac{12}{13}\)