Question

Classify the triangle by its angles and its sides. Given a triangle with angle measures of 90°, and side lengths of 8 in., 6 in., and 10 in.:

a. obtuse isosceles
b. equilateral equiangular
c. right isosceles
d. right scalene

Answer 1

The triangle with angles including 90° and side lengths of 8 in., 6 in., and 10 in. is a right scalene triangle, as it has one right angle and no equal sides.

Step-by-step explanation:

To classify the triangle with angles of 90°, and side lengths of 8 in., 6 in., and 10 in., we first check to see if one of the angles is a right angle, which is an angle of exactly 90 degrees. Since one angle is given as 90°, this is a right triangle. We then use the Pythagorean theorem, which states for a right triangle with legs a and b, and hypotenuse c, the relationship is a² + b² = c². To classify the triangle by its sides, we compare the lengths of the sides. Since all three side lengths are different, the triangle is scalene, meaning no sides are equal in length. Therefore, the correct classification of this triangle is a right scalene triangle.