Question

If the sides of triangle are $10\text{cm},5\sqrt{5}\text{cm}\&15\text{cm}$ and one angle of the triangle is ${50}^o$.
What is the smallest angle of the triangle?

• A. ${40}^o$
• B. ${50}^o$
• C. ${90}^o$
• D. None of the above.

Answer 1

The correct option is A ${40}^o$

We can see that ${10}^2+(5\sqrt{5}{)}^2=100+125=225={15}^2$

As the sum of the square of two sides is equal to the square of third side, hence it is a right triangle.

One angle of the triangle must be ${90}^o$ and one another angle is given as ${50}^o$

Hence, third angle of the triangle : ${180}^o-{50}^o-{90}^o={180}^o-{140}^o={40}^o$.

Smallest angle of the triangle is ${40}^o$