Find the measure of the angle with the greatest measure (picture provided)
Accepted Solution
A:
Answer: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°