Question

Find the value of a and b

Answer 1

your answer is B. I hope that this helps

Answer 2

The value of a is 14 unit and the value of b is
`6√(2)` unit

Step-by-step 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
`ABDE` 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
`AB=DE=8` unit , and
`AD=BE=6` 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,
`BE=EC=6` unit

Using trigonometric ratio; to find the value of b:

`\sin \theta =(perpendicular)/(Hypotenuse)`

∴ using trigonometric sine ratio in triangle BEC, we have

`\sin 45^(\circ) =(6)/(b)` or

`(1)/(√(2) )= (6)/(b)`

On Simplify:

`b=6√(2)` unit

and the value of a = DC = DE+EC=8+6=14 unit

Therefore, the value of a is 14 unit and b is
`6√(2)` unit