Question

Find the missing side or angle.
Round to the nearest tenth.

Answer 1

`b = 2.7`

Explanation:

Given:

< C = 53°

< B = 80°

a = 2

Required:

Find b

Solution:

The question given suggests we are given measures for a ∆.

To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.

=> A = 180 - (53 + 80) = 47°

Law of Sines:
`(a)/(sin(A) = (b)/(sin(B)`

Plug in the values into the formula

`(2)/(sin(47) = (b)/(sin(80)`

Cross multiply

`2*sin(80) = b*sin(47)`

Divide both sides by sin(47) to make b the subject of formula

`(2*sin(80))/(sin(47) = b`

`2.69 = b`

`b = 2.7` (nearest tenth)