Bethany used the steps below in an attempt to solve for angle B in triangle ABC.

4.1 cm

2.7 cm

4.5 cm

[Not drawn to scale]

4.12 - 4.52+2.72 - 2 (4.5) (2.7) cos B

4.1=4.5+2.7-24.3cos B

-3.1--24 3cOSB

0.1276 = COS B

Given that,

The area parameters are

A = 2.7 cm, B = 4.1 cm C = 4.5 cm

We want to find the angle extended by B.

Using cosine Rule

b² = a² + c² - 2ac•Cosθ

4.1² = 2.7² + 4.5² - 2 * 2.7 * 4.5• Cosθ

16.81 = 7.29 + 20.25 - 24.3•Cosθ

16.81 - 7.29 - 20.25 = - 24.3•Cosθ

-10.73 = - 24.3•Cosθ

Cosθ = - 10.73 / - 24.3

Cosθ = 0.4416

θ = Cos~1 (0.4416)

θ = 63.8°

The angle B is 63.8°