Question

A triangle having sides of 2, 2, and 3 contains _____.

a right angle
an obtuse angle
three acute angles

Answer 1

an obtuse angle

Explanation:

right away, we know by pyth th that it cannot have a right angle. this is because the hypotenuse does not equal the square root of the sum of the sides.

2^2 + 2 ^2 = 3^2 ?

4 + 4 = 9?

8 does not equal 9

secondly, if the sum of the squared sides is less than hypotenuse squared, the triangle has an obtuse angle.

2^2 + 2^2 < 3^2 ?

4 +4 < 9

8 < 9 , this is true, which means that the triangle has an obtuse angle

Answer 2

an obtuse angle

Explanation:

A right triangle with legs of length 2 would have a hypotenuse of length ...

√(2² +2²) = √8 ≈ 2.828

The third side of this triangle is longer than that, so the opposite angle must be more than 90°. This triangle contains an obtuse angle.

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A triangle solver says the angles are about 41.4°, 41.4°, and 97.2°.