Alright, lets get started.
Please refer the diagram I have attached.
In the lower triangle, two angles are given as 60° and 90°.
The third angle could be find by subtracting these two angle from 180°. (Because the sum of angles of a triangle is 180°)
So, the third angle would be = [tex] 180 - 60 - 90 [/tex]
Third angle would be = 30°
Now we could use SOH CAH TOA to find the side.
SOH means
[tex] sin 30 = \frac{opposite}{hypotenuse} [/tex]
Hypotenuse is given as 9√6 and opposite is x
we need to find x
[tex] sin 30 = \frac{x}{9\sqrt{6}} [/tex]
Putting the value of sin 30 as [tex] \frac{1}{2} [/tex]
[tex] \frac{1}{2} = \frac{x}{9\sqrt{6}} [/tex]
Cross multiplying
[tex] x = \frac{9\sqrt{6}}{2} [/tex]
[tex] x = 4.5\sqrt{6} [/tex] : Answer
Hope it will help :)
