Answer:
a = 18
b = 6√3
Step-by-step explanation:
WE can see in the diagram that there are two right angled triangles formed.
One with 45° angle as other interior angle and other with 60° interior angle.
So we will take the triangles one by one to find the required values.
As a is used in both triangles, first we will find the value of a using the left triangle.
In the triangle,
Hypotenuse = h = 18√2
θ = 45°
Using trigonometric ratio:
[tex]sin\ 45 =\frac{Perpendicular}{Hypotenuse}\\\frac{1}{\sqrt{2}}= \frac{a}{18\sqrt{2}}\\a = \frac{1}{\sqrt{2}} * 18\sqrt{2}\\a = 18[/tex]
Now in the right side triangle
θ1 = 60°
Perpendicular = a = 18
Base = b = ?
So,
[tex]tan\ 60 = \frac{perpendicular}{base}\\\sqrt{3} = \frac{\sqrt{18}}{b}\\b = \frac{18}{\sqrt{3}}\\b = \frac{6*3}{\sqrt{3}}\\b = \frac{6*\sqrt{3}*\sqrt{3}}{\sqrt{3}}\\b = 6\sqrt{3}[/tex]
Hence,
a = 18
b = 6√3
