Question

In triangle abc a b equal to 10 centimetre bc equal to 8 cm and ac is equal to 12 cm find the smallest angle

Answer 1

Before, movin' on towards the question we will recall the properties of inequalities of a triangle to understand it more quite easily.

Inequalities in a triangle : -

Theorem 1 : - If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).

Theorem 2 : - In any triangle, the side opposite to the larger (greater) angle is longer.

Theorem 3 : - The sum of any sides of  triangle is greater than the third side.

So now, we have recalled the theorems related to the inequalities of a triangle.

So now, movin' on towards our question, which is,

"In △ABC, AB = 10 cm, BC = 8 cm and AC = 12 cm. Find the smallest angle."

Solution : -

=> In △ABC,

AC < BC

= 12 cm < 8 cm

AB < BC

10 cm < 8 cm

AC < AB

12 cm < 10 cm

Therefore, AC is the longest side and BC is the shortest.

"So, angle opposite to the longest (greatest) side is greatest."

Here in △ABC,

∠ABC < ∠ACB

∠ABC < ∠BAC

∠ACB < ∠BAC

So, ∠ABC is the greatest angle and ∠BAC is the smallest angle.