Question

In Triangle ABC, B = 90° and AB = BC then AB : AC =

(a) 1:3
(b) 1:2
(c) 1:√2
(d) √2:1

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Answer 1

Answer:

1:√2

Step-by-step explanation:

let AB=BC=x

then AC = √2 x

AB:AC = x:√2 x

= 1 :√2

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Answer 2

Given :

In triangle ABC

• angle(B) = 90°
• AB = BC

To find :

AB : AC

Solution :

Let - AB = BC = a

As two sides are equal and one angle is 90° , therefore ∆ABC is right angle isosceles triangle.

This give angle(BCA) = angle(BAC) = 45°

Taking sine function of angle(BCA) , we get

➝ sin 45° = AB/AC

Note - sin (45°) = 1/√2

➩ 1/(√2) = AB/AC

➩ AB : AC = 1 : √2

Therefore answer is option c

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ANSWER :

Option c) 1 :√2