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navik [9.2K]
4 years ago
9

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

Mathematics
1 answer:
Morgarella [4.7K]4 years ago
6 0

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 \theta, then

\cos \theta = \frac{\sqrt{2} }{2\sqrt{2} }  = \frac{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)

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