Question

If the sides of a triangle are 15 cm, 12 cm, and 9 cm, then the greatest angle of the triangle is

• A. 90${}^0$
• B. 180${}^0$
• C. 60${}^0$
• D. 120${}^0$

Answer 1

The correct option is A 90${}^0$

Given, sides of the triangle are 15 cm, 12 cm and 9 cm.
From converse of pythagoras theorem, if the square of larger side of a triangle is equal to sum of squares of other two sides, then the triangle is a right triangle.
Now, 15${}^2$ = 225, 12${}^2$ = 144 and 9${}^2$ = 81
12${}^2$ + 9${}^2$ = 144 + 81
= 225
= 15${}^2$
So, the given triangle is a right triangle.
$\because$ Sum of angles of a triangle is 180${}^0$ and one angle in a right triangle is 90${}^0$
So, sum of other two angles = 90${}^0$
$\therefore$ The greatest angle in a right triangle is 90${}^0$