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ale4655 [162]
4 years ago
11

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

Mathematics
2 answers:
garri49 [273]4 years ago
8 0

Answer:

Obtuse triangle

Step-by-step explanation:

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

By an extension of the Pythagorean theorem:

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

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: <em>637.25 < 676</em>.

That means that this triangle is obtuse.

maria [59]4 years ago
4 0

Answer:

Obtuse

Step-by-step 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.

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