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CaHeK987 [17]
3 years ago
5

Calculate the side lengths a and b to two decimal places

Mathematics
1 answer:
muminat3 years ago
3 0

Answer:

Option (D)

Step-by-step explanation:

In the picture attached,

An obtuse angle triangle ABC has been given.

By applying Sine rule in the triangle,

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

Since, m∠A + m∠B + m∠C = 180°

45° + 110° + m∠C = 180°

m∠C = 180°- 155° = 25°

\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}

\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374

\frac{\text{Sin110}}{b}=0.060374

b = \frac{\text{Sin110}}{0.060374}

b = 15.56

b ≈ 15.56

\frac{\text{Sin45}}{a}=0.060374

a = \frac{\text{Sin45}}{0.060374}

a = 11.712

a = 11.71

Therefore, Option (D) will be the answer.

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