Question

Need help simple explanation if possible

Answer 1

Angle B = 30°

Angle A = 60°

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°

Answer 2

m < A = 60º

m < B = 30º

Explanation:

The given sides on this triangle are: 6,
`6√(3)`, and 12

Any triangle with the angles of 30º - 60º - 90º always has side lengths in this proportion:

x,
`x√(3)`, 2x

We can line this up with the given sides. If x is 6, then 2x would be 12.

x :
`x√(3)` : 2x = 6 :
`6√(3)` : 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
`x√(3)` (
`6√(3)` in this question) or 60º in the angle proportion.

This means that m < A = 60º

Let me know if you have any questions!