Question

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

Answer 1

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

Answer 2

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

Explanation:

In triangle QRP

PQ= 20

PR=12

QR= 16

`sin\theta= (perpendicular\; side )/(Hypotenuse)`

`sinP=(QR)/(PQ)`

`\therefore sinP=(16)/(20)`

`sinP=(4)/(5)`

sinQ=
`(PR)/(PQ)`

sinQ=
`(12)/(20)`

sinQ=
`( 3)/(5)`

In triangle STU

SU=16

UT=34

ST=30

sinU=
`(ST)/(TU)`

sinU=
`(30)/(34)`

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

sinT=
`(US)/(UT)`

sinT=
`(16)/(34)`

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

Hence, sinP=
`(4)/(5)`.