If the 3 sides of a triangle are a ,root 3a, 2a,, then find the measure of angle opposite to the longest side? PLZ GIVE AN DETAILED ANSWER PLZ
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Answered by
55
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. Obviously 90° is the greatest angle
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. Obviously 90° is the greatest angle
Answered by
30
Answer:
Step-by-step explanation:
(√3a)²=(√2a)²+a²
3a²=2a²+a²
3a²=3a²
by converse of pythagoras theorem √3s is the hypotenuse
the angle opp to the hyp is 90*
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