using the side lengths of △pqr and △stu, which angle has a sine ratio of $\frac{4}{5}$?\n∠p\n∠q\n∠t\n∠u
using the side lengths of △pqr and △stu, which angle has a sine ratio of $\frac{4}{5}$?\n∠p\n∠q\n∠t\n∠u
Answer
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 sides $PQ = 20$, $PR=12$, and $QR = 16$. For $\angle P$, $\sin P=\frac{QR}{PQ}=\frac{16}{20}=\frac{4}{5}$.
Step3: Analyze $\triangle STU$
In right - triangle $\triangle STU$ with sides $ST = 30$, $SU = 16$, and $TU = 34$. For $\angle T$, $\sin T=\frac{SU}{TU}=\frac{16}{34}=\frac{8}{17}$, for $\angle U$, $\sin U=\frac{ST}{TU}=\frac{30}{34}=\frac{15}{17}$.
Answer:
$\angle P$