ABC is a triangle in which BC = 10 cm, CA = 6 cm and AB = 8 cm. Which one of the following is correct?a)ABC is an acute angled triangleb)ABC is an obtuse angled trianglec)ABC is a right angled triangled)None of the aboveCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

To determine whether ABC is an acute, obtuse, or right-angled triangle, we can use the Pythagorean Theorem. Let's label the sides of the triangle as follows:
- BC = 10 cm
- CA = 6 cm
- AB = 8 cm
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's calculate the squares of the lengths of BC, CA, and AB:
- BC^2 = 10^2 = 100
- CA^2 = 6^2 = 36
- AB^2 = 8^2 = 64
Now, let's check if the Pythagorean Theorem holds true for these values:
- If BC^2 = CA^2 + AB^2, then ABC is a right-angled triangle.
- If BC^2 > CA^2 + AB^2, then ABC is an obtuse-angled triangle.
- If BC^2 < ca^2='' +='' ab^2,='' then='' abc='' is='' an='' acute-angled='' />
Using the above calculations, we find:
- BC^2 = 100
- CA^2 + AB^2 = 36 + 64 = 100
Since BC^2 = CA^2 + AB^2, ABC is a right-angled triangle.
Therefore, the correct answer is option C: ABC is a right-angled triangle.

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