Question

What are the angle measures of the triangle 6 12 6sqrt3?

Answer 1

The measure of angle A is 30 degree, measure of angle B is 90 degree and measure of angle C is 60 degree.

Explanation:

The measures of given sides are 6, 12,
`6√(3)`.

According to the Law of Cosine:

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

Using Law of Cosine, we get

`\cos A=((12)^2+(6√(3))^2-(6)^2)/(2(12)(6√(3)))`

`\cos A=(216)/(144√(3))`

`\cos A=(3)/(2√(3))`

`A=30^(\circ)`

Similarly,

`\cos B=(a^2+c^2-b^2)/(2ac)`

`\cos B=((6)^2+(6√(3))^2-(12)^2)/(2(6)(6√(3)))`

`\cos B=(0)/(36√(3))`

`\cos B=0`

`B=90^(\circ)`

Therefore, measure of angle A is 30 degree and measure of angle B is 90 degree.

According to angle sum property, the sum of interior angles of a triangle is 180 degree.

`A+B+C=180^(\circ)`

`30^(\circ)+90^(\circ)+C=180^(\circ)`

`C=60^(\circ)`

Therefore the measure of angle C is 60 degree.