Question

identifying trig ratios (diagram), level 1
question
express sin v as a fraction in simplest terms.
answer
attempt 1 out of 3
sin v =
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Explanation:

Step1: Recall the sine ratio formula

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Identify the sides relative to angle $V$

For $\angle V$, the opposite side is $TU$ and the hypotenuse is $TV$.
First, find $TU$ using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 30$ (hypotenuse $TV$) and $b = 18$ (side $UV$). Let $a=TU$. Then $a=\sqrt{30^{2}-18^{2}}=\sqrt{900 - 324}=\sqrt{576}=24$.
So, $\sin V=\frac{TU}{TV}$

Step3: Substitute the values

$\sin V=\frac{24}{30}=\frac{4}{5}$

Answer:

$\frac{4}{5}$