What are the angle measures of the triangle 6 12 - id61261544544, laurajwyman1952

Ответ:

leleee10

15.03.2022

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, $6\sqrt{3}$ .

According to the Law of Cosine:

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

Using Law of Cosine, we get

$\cos A=\frac{(12)^2+(6\sqrt{3})^2-(6)^2}{2(12)(6\sqrt{3})}$

$\cos A=\frac{216}{144\sqrt{3}}$

$\cos A=\frac{3}{2\sqrt{3}}$

$\cos A=\frac{\sqrt{3}{2}$

$A=30^{\circ}$

Similarly,

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\cos B=\frac{(6)^2+(6\sqrt{3})^2-(12)^2}{2(6)(6\sqrt{3})}$

$\cos B=\frac{0}{36\sqrt{3}}$

$\cos B=0$

$B=90^{\circ}$

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.

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