Question

What is the length of SR?

9 units
12 units
15 units
18 units

Answer 1

(C) 15 units

Explanation:

From the given figure, it is given that ST=9, TQ=16 and RT=x,

From ΔSRQ, we get

cosS=
`(RS)/(SQ)`

cosS=
`(RS)/(25)` (1)

Also, from ΔSTR, we have

cosS=
`(ST)/(RS)`

cosS=
`(9)/(RS)` (2)

From equations (1) and (2), we get

`(RS)/(25)=(9)/(RS)`

⇒
`(RS)^(2)=225`

⇒
`RS=15 units`

Thus, Option C is correct.

Answer 2

we know that

In the right triangle RSQ

`cos\ S=(RS)/(SQ)`

`cos\ S=(RS)/(25)` ------> equation
`1`

In the right triangle RST

`cos\ S=(ST)/(RS)`

`cos\ S=(9)/(RS)` ------> equation
`2`

equate equation
`1` and equation
`2`

`(RS)/(25)=(9)/(RS)\\ \\ RS^(2) =25*9\\ \\ RS=√(225) \\ \\ RS=15\ units`

therefore

the answer is

the length of SR is
`15\ units`