Question

In △ABC,a=11, b=20, and c=28. Find m∠A.

Answer 1

use cosine rule

a² = b² + c² -(2*b*c*cosA)

Answer 2

Answer:

About 18.36 degrees.

Step-by-step explanation:

We are going to use law of cosines since we are given the three side measurements.

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

$11^2=20^2+28^2-2(20)(28) \cos(A)$

$121=400+784-40(28) \cos(A)$

$121=1184-1120 \cos(A)$

Subtract 1184 on both sides:

$121-1184=-1120 \cos(A)$

$-1063=-1120 \cos(A)$

Divide both sides by -1120:

$\frac{-1063}{-1120}=\cos(A)$

$\frac{1063}{1120}=\cos(A)$

Take cosine's inverse on both sides:

$\cos^{-1}(\frac{1063}{1120})=A$

Put left side into calculator:

$18.36^\circ \approx A$