Answer:
The length of the missing side SR is 33.1 feet
Step-by-step explanation:
Let us revise the sine rule
In a triangle [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex] , where
- a is the side opposite to angle A
- b is the side opposite to angle B
- c is the side opposite to angle C
In Δ MSR
∵ MR is opposite to ∠S
∵ SR is opposite to ∠M
- By using the sine rule
∴ [tex]\frac{sinS}{MR}=\frac{sinM}{SR}[/tex]
∵ m∠S = 101°
∵ m∠M = 37°
∵ MR = 54 feet
- Substitute them in the statement of the ratio above
∴ [tex]\frac{sin(101)}{54}=\frac{sin(37)}{SR}[/tex]
- By using the cross multiplication
∴ SR × sin(101) = 54 × sin(37)
- Divide both sides by sin(101)
∴ SR = 33.10626661
- Round it to the nearest tenth
∴ SR = 33.1 feet
The length of the missing side SR is 33.1 feet
