Question

find the sine, cosine, and tangent of ∠v. simplify your answers and write them as proper fractions or numbers. sin(v) = cos(v) = tan(v) =

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle V$, the opposite side to $\angle V$ is $WX$, the adjacent side is $VW$, and the hypotenuse is $VX = 37$, $VW=12$.
First, find the length of $WX$ using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 37$ and $a = 12$. Let $b$ be the length of $WX$. Then $b=\sqrt{37^{2}-12^{2}}=\sqrt{(37 + 12)(37 - 12)}=\sqrt{49\times25}=\sqrt{49}\times\sqrt{25}=35$.

Step2: Calculate $\sin(V)$

$\sin(V)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{35}{37}$.

Step3: Calculate $\cos(V)$

$\cos(V)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{12}{37}$.

Step4: Calculate $\tan(V)$

$\tan(V)=\frac{\text{opposite}}{\text{adjacent}}=\frac{35}{12}$.

Answer:

$\sin(V)=\frac{35}{37}$, $\cos(V)=\frac{12}{37}$, $\tan(V)=\frac{35}{12}$