Respuesta :
The following set of numbers, 8, 15, and 17, can be the measures of the sides of a triangle, specifically a right triangle.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 8, b = 15, and c = 17
a + b > c 8 + 15 > 17 23 > 17 True
a + c > b 8 + 17 > 15 25 > 15 True
b + c > a 15 + 17 > 8 32 > 8 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
8^2 + 15^2 = 289
2. Compare it to the square of the largest side.
17^2 = 289
289 = 289
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 8, 15, and 17 can be the measure of the sides of a right triangle.
To learn more about types of triangle based on side lengths: brainly.com/question/13619935
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