Three sides of a triangle are, a, 3a, √10 a. Find the measurement of the angle opposite to the largest side

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Solution

We know that
In a right triangle, the sum of the squares of the any two sides is equal to the the square of the third side.

Observe that
a²+(3a)² = (side)²
⇒ a²+9a² = (side)²
⇒10a² = (side)²
side = √10 a

Therefore, the triangle is a right triangle.

The angle opposite to the the largest side is 90 degrees

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