Question

Find m∠A. Put the answer below. m∠A =

Answer 1

Angle A = 30 degrees

1) Use the Pythagorean Theorem: $a^{2} + b^{2} = c^{2}$

--> $12^{2} + (4\sqrt{3})^{2} = AC^{2}$

--> 144 + 48 = $AC^{2}$

--> 192 = $AC^{2}$

--> AC = $8\sqrt{3}$

2) Figuring out the type of triangle it is

There's a formula on the sides of a certain type of triangle:

--> Hypotenuse: a, Short Leg: a/2, Longer Leg: a/2 * $\sqrt{3}$

That type of triangle perfectly matches the sides of our triangle: 12, $4\sqrt{3}$, $8\sqrt{3}$

Therefore, this triangle is a 30, 60, 90 triangle.

3) Finding the measure of angle A

--> Angle B is given: 90 degrees

--> The angle that's between Sides AB and AC is 30 degrees

Finally, we can conclude that Angle A is 30 degrees