Question

What is the length of SR? 9 units 12 units 15 units 18 units

Answer 1

Answer:

(C) 15 units

Step-by-step explanation:

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

From ΔSRQ, we get

cosS=$\frac{RS}{SQ}$

cosS=$\frac{RS}{25}$                        (1)

Also, from ΔSTR, we have

cosS=$\frac{ST}{RS}$

cosS=$\frac{9}{RS}$                           (2)

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

$\frac{RS}{25}=\frac{9}{RS}$

⇒$(RS)^{2}=225$

⇒$RS=15 units$

Thus, Option C is correct.

Answer 2

we know that

In the right triangle RSQ

$cos\ S=\frac{RS}{SQ}$

$cos\ S=\frac{RS}{25}$ ------> equation $1$

In the right triangle RST

$cos\ S=\frac{ST}{RS}$

$cos\ S=\frac{9}{RS}$ ------> equation $2$

equate equation $1$ and equation $2$

$\frac{RS}{25}=\frac{9}{RS}\\ \\ RS^{2} =25*9\\ \\ RS=\sqrt{225} \\ \\ RS=15\ units$

therefore

the answer is

the length of SR is $15\ units$