A triangle has side lengths of 87 cm, 21cm, and 93 cm. Is the triangle acute, obtuse, or right?

The triangle that has side lengths of 87 cm, 21cm, and 93 cm is an obtuse triangle.

What is a triangle?

A triangle is a two dimensional geometrical figure that has three sides, three interior angles, and three vertices.

The three sides of the given triangle are 87 cm, 21cm, and 93 cm.

Now, (87)² + (21)²

= 7569 + 441

= 8010

≠ (93)²

Therefore, it is not a right-angle triangle.

Now, using cosine law:

(87)² = (21)² + (93)² + 2 × 21 × 93 cos Ф

⇒ 7569 = 441 + 8649 + 3906 cos Ф

⇒ 3906 cos Ф = (7569 - 441 - 8649)

⇒ 3906 cos Ф = - 1521

⇒ cos Ф = - 0.389

⇒ Ф = 112.92°

As an angle of the given triangle is 112.92°, then the given triangle is obtuse triangle.

Learn more about a triangle here: https://brainly.com/question/1603585

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