Given:
The figure of a right angle triangle.
Measure of one angle is 45 degrees.
Hypotenuse = [tex]9\sqrt{2}[/tex]
Opposite side of angle 45 degrees = a
To find:
The value of a.
Solution:
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
It can be rewritten as:
[tex]\sin \theta=\dfrac{Opposite}{Hypotenuse}[/tex]
For the given triangle,
[tex]\sin (45^\circ)=\dfrac{a}{9\sqrt{2}}[/tex]
[tex]\dfrac{1}{\sqrt{2}}=\dfrac{a}{9\sqrt{2}}[/tex]
[tex]\dfrac{9\sqrt{2}}{\sqrt{2}}=a[/tex]
[tex]9=a[/tex]
Therefore, the value of a is 9 units.
