Question

Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of Four-fifths?

∠P
∠Q
∠T
∠U

Answer 1

Answer:

$\angle P$

Step-by-step explanation:

Given

$\triangle PRQ = \triangle TSU = 90^o$

$PQ = 20$     $QR = 16$    $PR = 12$

$ST = 30$       $TU = 34$    $SU = 16$

See attachment

Required

Which sine of angle is equivalent to $\frac{4}{5}$

Considering $\triangle PQR$

We have:

$\sin(P) = \frac{QR}{PQ}$ --- i.e. opposite/hypotenuse

So, we have:

$\sin(P) = \frac{16}{20}$

Divide by 4

$\sin(P) = \frac{4}{5}$

Hence:

$\angle P$ is correct