Question

Calculate the side lengths a and b to two decimal places

A. a= 10.92 b=14.52 <--- My answer

B. a= 11 b= 15

C. a=4.18 b=3.15

D. a= 11.40 b=13.38

Answer 1

Option (D)

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.