Question

What is the measure of angleR to the nearest degree? TR-35 ST-30 S-69° •31° •53° •58° •80°​

Answer 1

In the diagram, the measure of angle R is 53°

Law of sines

From the question, we are to determine the measure of angle R

Using the law of sines, we can write that

$\frac{sin R}{r} =\frac{sin S}{s}$

In the given diagram,

r = 30

S = 69°

s = 35

Thus,

$\frac{sin R}{30} =\frac{sin 69^\circ}{35}$

$sin R =\frac{30 \times sin 69^\circ}{35}$

sin R = 0.8002

R = sin⁻¹(0.8002)

R = 53.149°

R ≈ 53°

Hence, the measure of angle R is 53°

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