Question

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

Answer 1

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°