Question

express cos y as a fraction in simplest terms.
answer
attempt 1 out of 2
cos y =
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Explanation:

Step1: Find the hypotenuse

In right triangle \( \triangle XYW \), by Pythagorean theorem, \( YW=\sqrt{XY^{2}+XW^{2}} \). Given \( XY = 6 \), \( XW = 8 \), so \( YW=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10 \).

Step2: Recall cosine definition

For angle \( Y \), \( \cos Y=\frac{\text{adjacent}}{\text{hypotenuse}} \). The adjacent side to \( Y \) is \( XY = 6 \), hypotenuse is \( YW = 10 \). So \( \cos Y=\frac{6}{10}=\frac{3}{5} \).

Answer:

\(\frac{3}{5}\)