Question

solve the question step by step​

Answer 1

Solution :

From the above question , we can gather that , ∆ ABC is a right angled triangle with angle B = 90° .

Now , it is also given that Angle A = 45° . According to the angle sum criterion , the sum of all the interior angles of any triangle add upto 180° .

So , angle A + angle B + angle C = 180°

=> 90° + 45° + angle C = 180° . Hence , Angle C is 45° . Now , we can observe that angle A = angle C . This shows that ∆ ABC is a right angled isosceles triangle with AB = AC .

Now , let AB = x cm . Applying the Pythagoras theorem here , AB² + AC² = ( 8√2 )²

=> x² + x² = 128

=> 2x² = 128

=> x² = 64

=> x = | ± 8 | = 8 cm .

Answer :

AB = 8 cm

_______________________

Answer 2

Step-by-step explanation:

In triangle ABC;

<ABC+ <BAC+ <ACB=180

90+45+ <ACB=180

135+ <ACB=180

<ACB=180-135=45

so triangle ABC is an isoseles triangle where AB=BC

By Pythagoras;

AB^2 +BC^2 =AC^2

AB^2 +AB^2=128

2×AB^2=128

AB^2=64

AB=8