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I need help determining if the following lengths of a given triangle is acute, right, or obtuse.

I need help determining if the following lengths of a given triangle is acute, right-example-1
User Vikramaditya
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1 Answer

10 votes
10 votes

Answer

a) 8, 10, 6

Right angle triangle.

b) 32, 19, 11

Not a triangle

c) 10, 24, 16

Obtuse triangle

Step-by-step explanation

To answer this question, we first explain what these type of triangles are

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

If the three sides in a triangle are a, b and c with c being the longest side.

When c² < a² + b²

The triangle is an acute triangle.

When c² = a² + b²

The triangle is a right angle triangle.

When c² > a² + b²

The triangle is an obtuse triangle.

But, it should be noted that if the longest side is equal to or more than the sum of the two sides, c ≥ a + b, the triangle is not possible.

So, we will take each of the questions one at a time

a) 8, 10, 6

a = 8

b = 6

c = 10 (longest side)

a² + b² = 8² + 6² = 64 + 36 = 100

c² = 100

100 = 100

c² = a² + b²

Hence, this triangle is a right angle triangle.

b) 32, 19, 11

a = 19

b = 11

c = 32 (longest side)

a + b = 19 + 11 = 30

c = 32

32 > 30

Hence, this triangle is not possible.

c) 10, 24, 16

a = 10

b = 16

c = 24 (longest side)

a² + b² = 10² + 16² = 100 + 256 = 356

c² = 24² = 576

576 > 356

c² > a² + b²

Hence, this triangle is an obtuse triangle.

Hope this Helps!!!

User CarlosE
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