Question

In AABC, MLA = 53, m4C = 84, and side a = 8 inches. Find the length of side b to the nearest tenth of an inch.

Answer 1

Answer:

6.8 inches

Step-by-step explanation:

Given data :

m∠ A = 53°  ,  m∠ C = 84° , side a = 8 inches

therefor m ∠ B = ( 180 - (84 + 53 )) = 43°

Find the length of side b

we will apply sine rule here

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

= $\frac{8}{sin53}$  = $\frac{b}{sin43}$

∴ b = ( sin43° * 8 ) / sin53°

      = ( 0.6819 * 8 ) / 0.7986

      = 5.4552 / 0.7986 = 6.83 ≈ 6.8 inches