Question

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

Answer 1

Answer:

$b = 2.7$

Step-by-step 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: $\frac{a}{sin(A} = \frac{b}{sin(B}$

Plug in the values into the formula

$\frac{2}{sin(47} = \frac{b}{sin(80}$

Cross multiply

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

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

$\frac{2*sin(80)}{sin(47} = b$

$2.69 = b$

$b = 2.7$ (nearest tenth)