Question

Triangle ABC has side lengths: √6, √2, and 2√2 units. The measures of the angles of the triangle would be... If the base of the triangle has a length of √6 then the measure of the base angle is...

Answer 1

The three sides given shows the it is a 30-60-90 right triangle. Since the base of sqrt (6) is the second largest number it would correspond to 60°.

Answer 2

Answer:

the measure of the angles are: ${\frac{\pi}{3},\frac{\pi}{6},\frac{\pi}{2}}$

Step-by-step explanation:

Let the side of the triangle ABC is given by a,b,c.

The measure of the angle is given by as depicted in the figure.

so let $a=\sqrt{6},b=\sqrt{2},c=2\sqrt{2}$

$A=\arccos(\frac{1}{2}), B=\arccos(\frac{\sqrt{3}}{2}) , C=\arccos (0)$

$A=\frac{\pi}{3},B=\frac{\pi}{6},C=\frac{\pi}{2}$

if the base of a triangle is $\sqrt{6}$, then let the base angle be some X.

$\cos (X)=\frac{\sqrt{6}}{2\sqrt{2}}$

where $\sqrt{6}$ is base and $2\sqrt{2}$ is hypotneuse.

$X=\arccos(\frac{\sqrt{3}}{2})$

$X=\frac{\pi}{6}$

so the measure of base angle when base length is $\sqrt{6}$ is $\frac{\pi}{6}$