In triangle ABC, AB=7, BC=10, and the measure of angle B=80, to the nearest 10th, what is b

Question

`in triangle ABC, AB=7, BC=10, and the measure of angle B=80, to the nearest 10th, what is b`

Answer 1

b = 11.0

Explanation:

From the given properties of the triangle,

b = AC

Applying the cosine rule, we have;

`b^(2)` =
`a^(2)` +
`c^(2)` - 2acCos B

=
`10^(2)` +
`7^(2)` - 2(10 x 7) Cos 80

= 100 + 49 - 140 x 0.17365

= 149 - 24.311

= 124.689

b =
`√(124.689)`

= 11.1664

b = 11.0