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

Explanation:

Step1: Find side length of TU using Pythagorean theorem

Let $TU = x$. By $a^{2}+b^{2}=c^{2}$, we have $x=\sqrt{34^{2}-16^{2}}=\sqrt{(34 + 16)(34 - 16)}=\sqrt{50\times18}=\sqrt{900}=30$.

Step2: Calculate sine of ∠V

$\sin(V)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{TU}{TV}=\frac{30}{34}=\frac{15}{17}$.

Step3: Calculate cosine of ∠V

$\cos(V)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{UV}{TV}=\frac{16}{34}=\frac{8}{17}$.

Step4: Calculate tangent of ∠V

$\tan(V)=\frac{\text{opposite}}{\text{adjacent}}=\frac{TU}{UV}=\frac{30}{16}=\frac{15}{8}$.

Answer:

$\sin(V)=\frac{15}{17}$, $\cos(V)=\frac{8}{17}$, $\tan(V)=\frac{15}{8}$