Question

use the diagram of triangle xyz to answer the questions. what is the length of side xy? what is the value of sin(x)? what is the value of cos(x)? what is the value of tan(x)?

Explanation:

Step1: Find length of XY using Pythagorean theorem

$XY=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10$

Step2: Calculate sin(X)

$\sin(X)=\frac{YZ}{XY}=\frac{8}{10}=\frac{4}{5}$

Step3: Calculate cos(X)

$\cos(X)=\frac{XZ}{XY}=\frac{6}{10}=\frac{3}{5}$

Step4: Calculate tan(X)

$\tan(X)=\frac{YZ}{XZ}=\frac{8}{6}=\frac{4}{3}$

Answer:

Length of XY: 10
sin(X): $\frac{4}{5}$
cos(X): $\frac{3}{5}$
tan(X): $\frac{4}{3}$