Solve the right triangle, ΔABC, for the missing side and angles to the nearest tenth given sides a = 13.2 and b = 17.7.

Side c = 22.1

Angle A = 36.7°

Angle B = 53.2°

Angle C = 90.1°

Step-by-step explanation:

Triangle ABC is a right angle

Where given sides

a = 13.2

b = 17.7

We can find c using Pythagoras Theorem

Pythagoras Theorem for a right angle triangle=

c² = a² + b²

c = √(a² + b²)

c = √(13.2² + 17.7²)

c = 22.08008

≈To the nearest tenth = 22.1

We can solve for Angles A, B, C using Cosine rule

Angle A

a² = b² + c² - 2bc × Cos A

Cos A = b² + c² - a²/2bc

A = Arc cos ( b² + c² - a²/2bc)

A = Arc cos ( 17.7² + 22.1² - 13.2²/2 × 17.7 × 22.1)

A = 36.67563°

≈ To the nearest tenth = 36.7°

Angle B

b² = a² + c² - 2ac × Cos B

Cos B = a² + c² - b²/2ac

B = Arc cos (a² + c² - b²/2ac)

B = Arc cos(13.2² + 22.1² - 17.7²/ 2 × 13.2 ×22.1)

B = 53.21647°

≈Approximately to the nearest tenth = 53.2°

Angle C

c² = a² + b² - 2ab × Cos C

Cos C = a² + b² - c²/2ab

C = Arc cos ( a² + b² - c²/2ab)

C = Arc cos ( 13.2² + 17.7² - 22.1²/2 × 13.2 × 17.7)

C = 90.1079°

≈ to the nearest tenth = 90.1°