Question

Triangle ABC has side lengths: V6, V2, and 2/2 units.

The measures of the angles of the triangle are
If the base of the triangle has a length of 16 then the measure of the base angle is

Answer 1

90°, 60°, and 30°

60°.

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
`\theta`, then

`\cos \theta = (√(2) )/(2√(2) )  = (1)/(2)`

Hence,
`\theta` = 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)