Question

if 3 sides of a trinagle are a,root 3 a, root 2 a then find the measure of the angle oposite to the longest side

Answer 1

Step-by-step explanation:

Given a=a ,b=√3a c=2a

Here 2a> √3a> a .

By cosine rule we have

CosC=a²+b²-c²/2ab

CosC=a²+(√3a)²-(2a)²/2(a)(√3a)

= a²+3a²-4a²/2√3a²

=0

CosC= 0

Cos90°= CosC .

The angle opposite to the longest side is the longest angle.

Here pythagoras theorem is valid ,so it is a right angled triangle. We find that 90° is the greatest angle

Answer 2

Answer:

90°

Step-by-step explanation:

By Pythagoras theorem,

a² + (√2a)²

= a ² + 2a²

= 3a²

So,

longest side is hypotenuse

Therefore,

opposite angle of the hypotenuse is90°

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