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HELPPP!! Calculate the side lengths a and b to two decimal places. (there is a picture included)

HELPPP!! Calculate the side lengths a and b to two decimal places. (there is a picture-example-1

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6 votes

Answer:

Option (D)

Explanation:

In the given triangle ABC,

Sum of all interior angles = 180°

m∠A + m∠B + m∠C = 180°

72° + 85° + m∠C = 180°

m∠C = 180 - 157

m∠C = 23°

By applying Sine rule in the triangle,


\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}


\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=\frac{\text{Sin23}}{6.2}


\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=0.06302


\frac{\text{Sin72}}{a}=0.06302

a =
\frac{\text{Sin72}}{0.06302} = 15.09


\frac{\text{Sin85}}{b}=0.06302

b =
\frac{\text{Sin85}}{0.06302}

b = 15.81

Therefore, option (D) will be the answer.

User Ella Sharakanski
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