Question

In the figure ABC=90° BAC=BCA=45° If AC=2√2,then find AB
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Answer 1

Answer:

Given in a triangle ABC, ∠ABC = 90°

∠BAC = ∠BCA = 45 °

side AC = 2\sqrt{2}

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}AC

2

=AB

2

+BC

2

⇒ (2 \sqrt{2} )^{2}(2

2

)

2

= AB^{2} + AB^{2}AB

2

+AB

2

[ in isosceles triangle the two side are equal ]

⇒ 4(2) = 2 AB^{2}AB

2

⇒ AB^{2} = \frac{8}{2}AB

2

=

2

8

⇒ AB^{2} =4AB

2

=4

⇒ AB = 2