Question

The triangle has side lengths of 25 in, 26in, and 3.5 in. Classify acute, obtuse, or right

Answer 1

Obtuse

Explanation:

Using law of cosine, we can find the angle between the shorter sides:

c² = a² + b² − 2ab cos C

26² = 25² + 3.5² − 2(25)(3.5) cos C

cos C ≈ -0.221

C ≈ 102.8°

102.8° is greater than 90°, so the triangle is obtuse.

Answer 2

Obtuse triangle

Explanation:

The longest side of the triangle is 26 in, so that will be the hypotenuse.

By an extension of the Pythagorean theorem:

1. Right triangle: a² + b² = c²
2. Acute triangle: a² + b² > c²
3. Obtuse triangle: a² + b² < c²

Where a and b are the legs, and c is the hypotenuse.

Plug in: 3.5² + 25² ₙ 26²

Powers: 12.25 + 625 ₙ 676

Add: 637.25 < 676.

That means that this triangle is obtuse.