find the sine, cosine, and tangent of $angle x$.\nsimplify your answers and write them as proper fractions…

Explanation:

Step1: Find side WY via Pythagoras

$$WY = \sqrt{XW^2 - XY^2} = \sqrt{26^2 - 10^2} = \sqrt{676 - 100} = \sqrt{576} = 24$$

Step2: Calculate sin(X) (opp/hyp)

$$\sin(X) = \frac{WY}{XW} = \frac{24}{26} = \frac{12}{13}$$

Step3: Calculate cos(X) (adj/hyp)

$$\cos(X) = \frac{XY}{XW} = \frac{10}{26} = \frac{5}{13}$$

Step4: Calculate tan(X) (opp/adj)

$$\tan(X) = \frac{WY}{XY} = \frac{24}{10} = \frac{12}{5}$$

Answer:

$\sin(X) = \frac{12}{13}$ $\cos(X) = \frac{5}{13}$ $\tan(X) = \frac{12}{5}$