Find the measure of the angle with the greatest measure (picture provided)

The measure of the greatest angle is about 81° ⇒ answer (b)

Step-by-step 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°

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