Question

In ABC, angle BAC=angle BCA=45, angle ABC=90, AC=2√2 then write the value of AB​

Answer 1

Answer:

AB=AC/√2

Step-by-step explanation:

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Answer 2

Given:

Angle BAC=angle BCA=45°

Angle ABC=90°

AC=2√2 units

To find:

The length of AB

Solution:

The required length of AB is 2 units.

Since the sides equal to opposite angles are equal, sides AB and BC are equal.

AB=BC (1)

The ΔABC is a right-angled triangle and so the AB and BC's squares' sum will be equal to the square of AC.

Using the Pythagoras theorem,

$AB^{2} +BC^{2} =AC^{2}$

Using (1),

2$AB^{2}$=$AC^{2}$

2$AB^{2}$=$(2\sqrt{2}) ^{2}$

2$AB^{2}$=8

$AB^{2}$=4

AB=2 units

So, BC=2 units

Therefore, the required length of AB is 2 units.