Question

Triangle ABC is described below. Find all possible values for B, C, and c.

A= 121.59, a = 27.9 cm, b = 52.6 cm
Apply the rules regarding the use of significant digits to each angle and
length after all computations are complete.

Answer 1

c = 27.9

B = 62.13°

C = 89.90°

Explanation:

We are given the following values:

A= 121.59°, a = 27.9 cm, b = 52.6 cm

a) Finding side c

We would use Pythagoras Theorem

c² = a² + b²

c = √(a² + b²)

c = √(27.9² + 52.6²)

c = 59.54cm

≈ Approximately = 59.5cm

b) Finding B

We would be using Cosine rule to find Angle B

Cos B = a² + b² - c²/2ab

B = arc cos ( a² + c² - b²/2ac)

B = arc cos( 27.9² + 59.5² - 52.6²/ 2 × 27.9 × 59.5)

B = 62.13268°

B = 62.13°

c) Finding C

We would be using Cosine rule to find Angle C

Cos C = a² + b² - c²/2ab

C = arc cos ( a² + b² - c²/2ab)

C = arc cos( 27.9² + 52.6² - 59.5²/ 2 × 27.9 × 52.6)

C = 89.9°