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Give the angle classification of the triangle
with side lengths 3 cm, 5 cm, and 7 cm.

Sagot :

Given:

The sides of a triangle are 3 cm, 5 cm, 7 cm.

To find:

The angle classification of the given triangle.

Solution:

Let a,b,c are the three sides of a triangle ABC, where c is the longest side.

1. Triangle ABC is acute, if [tex]c^2<a^2+b^2[/tex].

2. Triangle ABC is acute, if [tex]c^2=a^2+b^2[/tex].

3. Triangle ABC is acute, if [tex]c^2>a^2+b^2[/tex].

The sum of square of two smaller sides is

[tex]3^2+5^2=9+25[/tex]

[tex]3^2+5^2=34[/tex]

In the given triangle 7 cm is the longest sides. So,

[tex]7^2=49[/tex]

It means,

[tex]7^2>3^2+5^2[/tex]

Since [tex]c^2>a^2+b^2[/tex], therefore, the triangle ABC is an acute triangle.

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