Question

A guide into how to use law of sines or cosines would be greatly appreciated.

Answer 1

RS = 22.5 feet, RT = 12.5 feet, and <R =
`34^(o)`

Explanation:

Cosine rule can be applied only when given the three sides of a triangle, or two sides and an included angle. Otherwise, sine rule is applied.

i. <R + <T + <S = 180 (sum of angles in a triangle)

<R + 116 + 30 = 180

<R = 180 - 146

= 34

<R =
`34^(o)`

In the given question, since we have two angles and one side we apply the sine rule.

ii.
`(ST)/(Sin R)` =
`(RS)/(Sin T)`

`(14)/(Sin 34)` =
`(RS)/(Sin 116)`

RS =
`(14*0.8988)/(0.5592)`

= 22.5021

RS = 22.5 feet

iii. Also,

`(ST)/(Sin R)` =
`(RT)/(Sin S)`

`(14)/(Sin 34)` =
`(RT)/(Sin 30)`

RT =
`(14*Sin 30)/(Sin 34)`

=
`(14*0.5)/(0.5592)`

= 12.5179

RT = 12.5 feet

Thus,

RS = 22.5 feet, RT = 12.5 feet, and <R =
`34^(o)`.