Answer:
RS = 22.5 feet, RT = 12.5 feet, and <R = [tex]34^{o}[/tex]
Step-by-step 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 = [tex]34^{o}[/tex]
In the given question, since we have two angles and one side we apply the sine rule.
ii. [tex]\frac{ST}{Sin R}[/tex] = [tex]\frac{RS}{Sin T}[/tex]
[tex]\frac{14}{Sin 34}[/tex] = [tex]\frac{RS}{Sin 116}[/tex]
RS = [tex]\frac{14*0.8988}{0.5592}[/tex]
= 22.5021
RS = 22.5 feet
iii. Also,
[tex]\frac{ST}{Sin R}[/tex] = [tex]\frac{RT}{Sin S}[/tex]
[tex]\frac{14}{Sin 34}[/tex] = [tex]\frac{RT}{Sin 30}[/tex]
RT = [tex]\frac{14*Sin 30}{Sin 34}[/tex]
= [tex]\frac{14*0.5}{0.5592}[/tex]
= 12.5179
RT = 12.5 feet
Thus,
RS = 22.5 feet, RT = 12.5 feet, and <R = [tex]34^{o}[/tex].
