Answer:
m∠A = 39.5°
Step-by-step explanation:
* Lets revise how to find the measure of an angle by using the cosine rule
- In any triangle ABC
# ∠A is opposite to side a
# ∠B is opposite to side b
# ∠C is opposite to side c
- The cosine rule is:
# a² = b² + c² - 2bc × cos(A)
# b² = a² + c² - 2ac × cos(B)
# c² = a² + b² - 2ab × cos(C)
- To find the angles use this rule
# m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]
# m∠B = [tex]cos^{-1}\frac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]
# m∠C = [tex]cos^{-1}\frac{a^{2}+b^{2}-c^{2}}{2ab}[/tex]
* Lets solve the problem
∵ a = 14 , b = 17 , c = 22
∵ m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{17^{2}+22^{2}-14^{2}}{2(17)(22)}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{289+484-196}{748}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{577}{748}[/tex]
∴ m∠A = 39.5°
