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

Explanation:

Step1: Calculate side XW (Pythagoras)

$$XW = \sqrt{XV^2 - WV^2} = \sqrt{45^2 - 27^2} = \sqrt{2025 - 729} = \sqrt{1296} = 36$$

Step2: Find sin(V) (opp/hyp)

$$\sin(V) = \frac{XW}{XV} = \frac{36}{45} = \frac{4}{5}$$

Step3: Find cos(V) (adj/hyp)

$$\cos(V) = \frac{WV}{XV} = \frac{27}{45} = \frac{3}{5}$$

Step4: Find tan(V) (opp/adj)

$$\tan(V) = \frac{XW}{WV} = \frac{36}{27} = \frac{4}{3}$$

Answer:

$\sin(V) = \frac{4}{5}$ $\cos(V) = \frac{3}{5}$ $\tan(V) = \frac{4}{3}$