169k views
2 votes
In △ABC,a=14, b=17, and c=22. Find m∠A.

1 Answer

2 votes

Answer:


\large\boxed{m\angle A\approx39^o}

Explanation:

Use the cosine law:


a^2=b^2+c^2-2bc\cos A

We have:


a=14,\ b=17,\ c=22

Substitute:


14^2=17^2+22^2-2(17)(22)\cos A\\\\196=289+484-748\cos A\\\\196=773-748\cos A\qquad\text{subtract 773 from both sides}\\\\-577=-748\cos A\qquad\text{divide both sides by (-748)}\\\\\cos A=(577)/(748)\\\\\cos A\approx0.7714\to m\angle A\approx39^o

User Stevebot
by
6.8k points