Question

In a figure angle ABC=90°angle BAC=BCA=45°If AC =2√2 then find AB​

Answer 1

Step-by-step explanation:

In ∆ABC,AngleA=45°,angleC=45°

AC=2√2

Therefore by 45°-45°-90° theorem

AB=1/√2×AC

=1/√2×2√2

=2Units

Therefore,AB=2 units

Answer 2

Answer:

In triangle ABC, AB = 2

Step-by-step explanation:

Given in a triangle ABC,  ∠ABC = 90°

                           ∠BAC = ∠BCA = 45 °

                                    side  AC  = 2$\sqrt{2}$

the triangle has 90° angle  ⇒ ABC is a right angle triangle

two angles are 45° and same  ⇒ ABC is a Isosceles triangle

Triangle ABC is an Isosceles right angle triangle                                        

by Pythagoras' theorem   $AC^{2} =AB^{2} +BC^{2}$

⇒  $(2 \sqrt{2} )^{2}$ = $AB^{2} + AB^{2}$  [ in isosceles triangle the two side are equal ]

⇒  4(2)  = 2 $AB^{2}$

⇒ $AB^{2} = \frac{8}{2}$

⇒ $AB^{2} =4$

⇒ AB = 2