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Step-by-step explanation:

Considering the small triangle in which the one side and two angles are given:

Finding the third angle of the small triangle

Sum of angles of the triangle is °

as two angles are given i.e 90° and 45°, so third angle is 180°-(90°+45°)

Third angle in the small triangle is 45°.

As the opposite angles are 45° joining together to form 90° angle, therefore the small triangle is an isosceles triangle in which the opposite sides are equal.

Therefore the two sides are 7 and 7 of small triangle, so By Pythagoras theorem the third side is

Similarly the bigger triangle is also an isosceles triangle whose base is determined i.e   = perpendicular length of bigger triangle.

Applying the Pythagoras theorem in bigger triangle:

8

step-by-step explanation:

just put √(2) * √(32) into a calculator. that will make the answer be 8.