Answer:
The measure of the greatest angle is about 81° ⇒ answer (b)
Explanation:
* Let the given triangle is ΔABC where,
- a = 18 inches ⇒ opposite to angle A
- b = 21 inches ⇒ opposite to angle B
- c = 14 inches ⇒ opposite to angle C
∵ The greatest angle is opposite to the largest side
∴ The greatest angle will be angle B because b is the largest side
* By using cos Rule:
∵ b² = a² + c² - 2ac cos(B)
* Lets re-arrange the terms to find the measure of angle B
∴ 2ac cos(B) = a² + c² - b²
∴ cos(B) = (a² + c² - b²)/2ac
∴ cos(B) = (18² + 14² - 21²)/2(18)(14) = 79/504
∴ m∠B = 80.98 ≅ 81°
∴ The measure of the greatest angle is about 81°