Triangle ABC has side lengths: V6, V2, and 2/2 units.The measures of the angles of the triangle areIf the base of the triangle has a length of 16 then the measure of the base angle is

Answer:90°, 60°, and 30°60°.Step-by-step explanation:The triangle ABC has side lengths √6, √2, and 2√2 units.It is clear that the triangle ABC is right triangle because (2√2)² = (√6)² + (√2)² that means the side lengths satisfy the Pythagoras Theorem.Now, if the angle between hypotenuse (2√2 units) and base (√2 units) is [tex]\theta[/tex], then [tex]\cos \theta = \frac{\sqrt{2} }{2\sqrt{2} }  = \frac{1}{2}[/tex]Hence, [tex]\theta[/tex] = 60°Therefore, the three angles of the triangle are 90°, 60°, and 30°.Now, if the base of the triangle is 16 units, then other two side lengths will also change proportionally to remain the triangle a right triangle.And in that case the base angle will remain 60°. (Answer)