determine if the following side lengths create an acute, obtuse, or right triangle. a) 20, 21, 28 b) 3, 6, 4 c) 8, 12, 15

a) 20, 21, 28 : acute

b) 3, 6, 4 : obtuse

c) 8, 12, 15 : obtuse

Step-by-step explanation:

You can see if a triangle is acute, obtuse, or right using the Pythagorean theorem as follows:

If , then the triangle is right.

If , then the triangle is acute.

If , then the triangle is obtuse.

Solve each to find if the given lengths form an acute, obtuse, or right triangle ( The biggest number is the hypotenuse length, since the hypotenuse is always the longest side in a triangle. This is represented by c):

a) 20, 21, 28

Insert numbers, using 28 as c:

_

Simplify exponents ():

_

Simplify addition:

_

Identify relationship:

The sum of the squares of a and b is greater than the square of c. This triangle is acute.

b) 3, 6, 4

Insert numbers, using 6 as c:

_

Simplify exponents:

_

Simplify addition:

_

Identify relationship:

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

c) 8, 12, 15

Insert numbers, using 15 as c:

_

Simplify exponents:

_

Simplify addition:

_

Identify relationship:

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

:Done.

98%

step-by-step explanation:

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