Question

If x equals 6, what is the order of the angles from smallest to largest degree?

Answer 1

Answer:

∠B < ∠A < ∠C

Step-by-step explanation:

Given,

In triangle ABC,

$AB=x^2+\frac{x}{2}$

$BC=x^2+\frac{x}{3}$

$CA=x^2-\frac{x}{2}$

At x = 6,

$AB=6^2+\frac{6}{2}=36 + 3 = 39$

$BC=6^2+\frac{6}{3}=36 + 2 = 38$

$CA=6^2-\frac{6}{2}=36 - 3 = 33$

We know that in a triangle, the interior angle opposite to largest side is largest, opposite to smallest side is smallest and opposite to medium side is medium.

Here, CA < BC < AB

Also, angles A, B and C are opposite angles of the sides BC, CA and AB respectively,

Hence, ∠B < ∠A < ∠C

Which is the required order of angles.

Answer 2

The size of the angle is always corresponding to the opposite side to it, for example
∠A corresponds to side BC
∠C corresponds to side AB
∠B corresponds to side AC
thus given x=6 then:
AC=x^2-x/2=33
AB=x^2+x/2=39
BC=x^2+x/3=34
thus the order of angles from the smallest to the largest is ∠B, ∠A, ∠C