Question

"Question43
In the adjoining figure, ΔABC is right - angled at B and Angle A = 45° . If AC = 3√2 cm, find (1)BC ,(2)AB .
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 290"

Answer 1

Hey there !

Given the triangle is Right angled at B,
So Angle B = 90°

Hypotenuse = AC = 3√2 cm.


Now, We will need to find BC, AB and We know that A = 45°

Apply cosine.

cosA = cos45

cosA = 1/√2

Now,
cosA = adjacent side to A / Hypotenuse

cosA = AB / AC

1/√2 = AB / 3√2

AB = 3√2 / √2 = 3cm .

Also, apply sine

sinA = sin45

sinA = 1/√2

We know that,
sinA = Opposite side of A / Hypotenuse

1/√2 = BC / AC

1/√2 = BC / 3√2

BC = 3cm .

$\therefore$ BC = 3 cm, AB = 3cm.

Quick hint : BC = AB as the triangle is isosceles triangle ( 45 , 45 , 90 : 2 angles are equal)

Hope helped!

Answer 2

solution.

Here,

1) sin 45°= BC/ 3√2

=> 1/√2 = BC/3√2

=> BC = 3*2cm =6 cm

2) tan 45° = AB / 3√2

=> 1 = AB /3√2

=> AB = 3√2 cm

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