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

`\angle P`

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
`(4)/(5)`

Considering
`\triangle PQR`

We have:

`\sin(P) = (QR)/(PQ)` --- i.e. opposite/hypotenuse

So, we have:

`\sin(P) = (16)/(20)`

Divide by 4

`\sin(P) = (4)/(5)`

Hence:

`\angle P` is correct