Question

using the side lengths of △pqr and △stu, which angle has a sine ratio of 4/5? ∠p ∠q ∠t ∠u

Explanation:

Step1: Recall sine - ratio definition

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Analyze $\triangle PQR$

In right - triangle $\triangle PQR$ with right - angle at $R$, if we consider an angle, for example, $\angle Q$, $\sin Q=\frac{PR}{PQ}$. Given $PR = 12$ and $PQ=20$, then $\sin Q=\frac{12}{20}=\frac{3}{5}$.

Step3: Analyze $\triangle STU$

In right - triangle $\triangle STU$ with right - angle at $S$, if we consider $\angle T$, $\sin T=\frac{SU}{TU}$. Given $SU = 24$ and $TU = 30$, then $\sin T=\frac{24}{30}=\frac{4}{5}$.

Answer:

B. $\angle T$