Question

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

Answer 1

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.