Answer:
The measure of angle A is 30 degree, measure of angle B is 90 degree and measure of angle C is 60 degree.
Step-by-step explanation:
The measures of given sides are 6, 12, [tex]6\sqrt{3}[/tex].
According to the Law of Cosine:
[tex]\cos A=\frac{b^2+c^2-a^2}{2bc}[/tex]
Using Law of Cosine, we get
[tex]\cos A=\frac{(12)^2+(6\sqrt{3})^2-(6)^2}{2(12)(6\sqrt{3})}[/tex]
[tex]\cos A=\frac{216}{144\sqrt{3}}[/tex]
[tex]\cos A=\frac{3}{2\sqrt{3}}[/tex]
[tex]\cos A=\frac{\sqrt{3}{2}[/tex]
[tex]A=30^{\circ}[/tex]
Similarly,
[tex]\cos B=\frac{a^2+c^2-b^2}{2ac}[/tex]
[tex]\cos B=\frac{(6)^2+(6\sqrt{3})^2-(12)^2}{2(6)(6\sqrt{3})}[/tex]
[tex]\cos B=\frac{0}{36\sqrt{3}}[/tex]
[tex]\cos B=0[/tex]
[tex]B=90^{\circ}[/tex]
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.
[tex]A+B+C=180^{\circ}[/tex]
[tex]30^{\circ}+90^{\circ}+C=180^{\circ}[/tex]
[tex]C=60^{\circ}[/tex]
Therefore the measure of angle C is 60 degree.
