Question

#3

Answer 1

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 $\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$ , 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

∴ $\frac{sinS}{MR}=\frac{sinM}{SR}$

∵ m∠S = 101°

∵ m∠M = 37°

∵ MR = 54 feet

- Substitute them in the statement of the ratio above

∴ $\frac{sin(101)}{54}=\frac{sin(37)}{SR}$

- 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