Question

Triangle ABC is an isosceles triangle with AC = BC. If AB^2=2AC^2, then find angle c​

Answer 1

Answer:

Step-by-step explanation:

There are several ways to answer this question.

Method1: It's given that AB²=2AC²  

And it can be written as  AB²=AC²+BC²  ( since  AC=BC  ) . It follows Pythagorean theorem. From this we can conclude that it is a right angled triangle with right angle at C. Hence angle C=90 °.

Method 2: By using cosine rule,

cosC=(BC²+AC²−AB²)/(2BC.AC)  

We know that  AB²=2AC²  and BC²=AC² , therefore  BC²+AC²−AB²=0 .

So  cosC=0  and therefore angle  C=90 °.

Answer 2

Answer:

In △ABC

(AB)2=2(AC)2

(AB)2=(AC)2+(AC)2

∵AC=BC

(AB)2=(AC)2+(BC)2

∴∠C=90∘

And △ABC is a right angle triangle

Step-by-step explanation:

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