Answer:
The value of a is 14 unit and the value of b is [tex]6\sqrt{2}[/tex] unit
EXPLANATION:
Draw a perpendicular line from vertex B to DC at E.
Labeling the diagram as shown in the attachment:
Now, as you can see from the Figure as shown in the attachment that [tex]ABDE[/tex] represents the rectangle because a rectangle is a quadrilateral with four right angles and their opposite sides would be parallel.
Therefore, we have the sides [tex]AB=DE=8[/tex] unit , and [tex]AD=BE=6[/tex] unit.
Consider the right triangle BEC
BY 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
therefore, the length of side, [tex]BE=EC=6[/tex] unit
Using trigonometric ratio; to find the value of b:
[tex]\sin \theta =\frac{perpendicular}{Hypotenuse}[/tex]
∴ using trigonometric sine ratio in triangle BEC, we have
[tex]\sin 45^{\circ} =\frac{6}{b}[/tex] or
[tex]\frac{1}{\sqrt{2} }= \frac{6}{b}[/tex]
On Simplify:
[tex]b=6\sqrt{2}[/tex] unit
and the value of a = DC = DE+EC=8+6=14 unit
Therefore, the value of a is 14 unit and b is [tex]6\sqrt{2}[/tex] unit
