By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides.
The triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is acute angle triangle.
How to find the type of triangle?
By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides. Thus,
- For a triangle to be right angle triangle,
[tex]c^2=a^2+b^2[/tex]
By this law it is observed that,
- For a triangle to be acute angle triangle,
[tex]c^2<(a^2+b^2)[/tex]
- For a triangle to be obtuse angle triangle,
[tex]c^2>(a^2+b^2)[/tex]
The sides of the given triangle are 3.8 cm ,3.7 cm, and 5 cm.
Here the longest side is 5 cm. Thus check the type of triangle using above formula. Longest side,
[tex]c^2=5^2\\c^2=25[/tex]
Other two sides,
[tex]a^2+b^2=3.8^2+3.7^2\\a^2+b^2=14.44+13.69\\a^2+b^2=28.13[/tex]
Therefore,
[tex]25<28.13\\[/tex]
Hence the triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is acute angle triangle.
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