Question

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$\huge\sf\red{Question}$

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If AC > AB > BC for ΔABC, then ∠ABC is always greater than

A)30° B)45° C)90° D)60° ​

$\sf\bold{Explanation \:is\: must }$​

Answer 1

60 (D)

Step-by-step explanation:

triangle is obtuse angle

Answer 2

Answer:

Option D

Step-by-step explanation:

Given :-

AC > AB > BC in ΔABC

To find :-

The value of ∠ABC is always greater than----

A)30° B)45° C)90° D)60°

Solution :-

Given that

In ∆ ABC , AC > AB > BC

It is clear that

It is not an equilateral triangle.

So the angles are not equal to 60° each.

and

AC> AB => AC² > AB²-----(1)

and

AC > BC => AC² > BC²-----(2)

on adding (1)&(2)

AC²+AC² > AB² + BC²

=> 2AC² > AB² +BC² ------(3)

We know that

In ∆ ABC, If AC² = AB² + BC² then it is a right angled triangle.

So above (3) we conclude that

No angle is not equal to 90°

Now

AC> BC> AB We conclude that

It is a scalene triangle .

So the angles depends upon the lengths of the sides

Now

AC> BC => ∠B > ∠A

AC > AB => ∠B > ∠C

=> ∠B > ∠A and ∠C

and

AB >BC => ∠C > ∠A

So, The angles are ∠B > ∠C > ∠A

We know that

The sum of all angles in a triangle is 180°

From all above possibilities ,

The angle B is always greater than 60°

=> ∠ABC is always greater than 60°.

Answer :-

∠ABC is always greater than 60° for the given problem.

Used formulae:-

→ The sum of all angles in a triangle is 180°