Question

In triangle RST, RT = 16, ST = 24, and m< R = 120. To the nearest tenth, what is m < s ?

Answer 1

m<S =
`35.3^(o)`

Explanation:

Applying the sine rule to the given question, we have;

`(r)/(Sin R)` =
`(s)/(Sin S)`

`(24)/(Sin 120)` =
`(16)/(Sin S)`

cross multiply to have,

16 x Sin 120 = 24 x Sin S

16 x 0.8660 = 24 Sin S

13.856 = 24 Sin S

Sin S =
`(13.856)/(24)`

= 0.57733

S =
`Sin^(-1)` 0.57733

= 35.2630

Thus, m<S =
`35.3^(o)`