Question

Find m∠A given ΔABC where a=4, b=6, c=3.

Answer 1

For this question, we're going to use the law of cosines.
The law of cosines is the following equation:

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

We know the values of a, b, and c. We want to find the measure of angle A.
$a=4$
$b=6$
$c=3$

Now, plug in these values into the equation.

$4^2=6^2+3^2-2(3)(6) \cos(A)$
$16=45-36 \cos(A)$

Add both sides by $36 \cos(A)$ and subtract both sides by 16

$36 \cos(A)=29$

Divide both sides by 36

$\cos(A)= \dfrac{29}{36}$

Take the inverse cosine, or arc cosine, of both sides.
Using a calculator, you'll get the following result.

$A \approx 36.3^O$

The measure of angle A should be 36.3 degrees. Hope this helps! :)