Question

Using the side lengths of pqr and stu which angle has a sine ratio of 4/5

Answer 1

Answer:

$sin P=\frac{4}{5}$.

Step-by-step explanation:

In triangle QRP

PQ= 20

PR=12

QR= 16

$sin\theta= \frac{perpendicular\; side }{Hypotenuse}$

$sinP=\frac{QR}{PQ}$

$\therefore sinP=\frac{16}{20}$

$sinP=\frac{4}{5}$

sinQ=$\frac{PR}{PQ}$

sinQ=$\frac{12}{20}$

sinQ=$\frac{ 3}{5}$

In triangle STU

SU=16

UT=34

ST=30

sinU=$\frac{ST}{TU}$

sinU=$\frac{30}{34}$

sinU=$\frac { 15}{17}$

sinT=$\frac{US}{UT}$

sinT=$\frac{16}{34}$

sinT=$\frac {8}{17}$

Hence, sinP=$\frac{4}{5}$.

Answer 2

Sin = Opp/Hypo
so
sin P = 16/20 = 4/5