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 formula

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 $\angle P$, $\sin P=\frac{QR}{PQ}$. Given $QR = 16$ and $PQ=20$, then $\sin P=\frac{16}{20}=\frac{4}{5}$.

Step3: Analyze $\triangle STU$

In right - triangle $\triangle STU$ with right - angle at $S$, $\sin T=\frac{SU}{TU}=\frac{16}{34}=\frac{8}{17}$, $\sin U=\frac{ST}{TU}=\frac{30}{34}=\frac{15}{17}$.

Answer:

$\angle P$