Question

In △ABC,a=14, b=17, and c=22. Find m∠A.

Answer 1

`\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`