Question

In triangle ABC, a = 9, c = 5, and angle B = 120°. Find the measure of angle A to the nearest degree. Show your work.

Answer 1

Answer:

39 degrees

Step-by-step explanation:

Answer 2

Answer:

Angle A = 39°

Step-by-step explanation:

We are given that there is a triangle ABC where a = 9, c = 5 and angle B = 120° and we are to find the measure of angle A.

But first we need to find the side b using the law of cosine:

$b^2 = a^2 + c^2- 2a*c*cos(120)$

$b^2 = 81 + 25 - 2*9*5*(-0.5)$

$b=\sqrt{151}$

Now finding angle A using law of cosine:

$cos(A) = \frac{b^2+c^2-a^2}{2b*c}$

$cos(A) = \frac{151+25-81}{2*12.29*5}$

$cos A=0.7730$

$A=39.38$

Therefore, the measure of angle A = 39°.