Need help simple explanation if possible

Answer:
m < A = 60º
m < B = 30º
Step-by-step explanation:
The given sides on this triangle are: 6, [tex]6\sqrt{3}[/tex], and 12
Any triangle with the angles of 30º - 60º - 90º always has side lengths in this proportion:
x, [tex]x\sqrt{3}[/tex], 2x
We can line this up with the given sides. If x is 6, then 2x would be 12.
x : [tex]x\sqrt{3}[/tex] : 2x = 6 : [tex]6\sqrt{3}[/tex] : 12
Angle B is across from 6, the shortest side. That also means that it corresponds to x, or the smallest angle in the proportion, 30º.
m < B = 30º
Solving for < A:
Method 1) Sum of Angles in a Triangle
Since we already know that one angle is right and therefore 90º and m < B is 30º, we can subtract these from the total sum of angle measures in a triangle to get the last angle, < A.
180º - 90º - 30º = 60º
m < A = 60º
Method 2) Using the second part of the proportion
Since m < A is across from the second largest side, we know that it is equal to [tex]x\sqrt{3}[/tex] ([tex]6\sqrt{3}[/tex] in this question) or 60º in the angle proportion.
This means that m < A = 60º
Let me know if you have any questions!
Angle B = 30°
Angle A = 60°
Step-by-step explanation:
There are a few ways you can find this. I'll use sine rule to find angle B then 180° minus the 90° + angle B to get angle A.
Using Sine Rule:
(Sin90)/12 = SinB/6
Multiply both side by 6 to get SinB by itself
(6Sin90)/12 = SinB
Send the sine across the equal sign to get B by itself
Sin becomes Sine Inverse (Asin or Sin-1)
Sin-1 (6Sin90/12) = B
Therefore B = 30° (from calculator)
Since the sum of interior angles in a triangle is 180°
it is safe to say:
Angle A + Angle B + Angle C = 180°
substitute in Angle B and C to find for A
Angle A + 30° + 90° = 180°
Angle A + 120° = 180°
Minus 120° from both side to get Angle A by Itself
Angle A = 180° - 120°
Angle A = 60°