Answer:
Explanation:
You want the shortest and longest sides of a 30°-60°-90° triangle that has a middle-length side that is 9√3 units.
Special right triangle
The triangle shown is one of two "special" right triangles. The sides have the ratios ...
1 : √3 : 2
If you multiply this set of ratios by 9, you get ...
9 : 9√3 : 18 = x : 9√3 : y
This tells you ...
x = 9
y = 18
__
Additional comment
The other "special" right triangle is the isosceles right triangle: 45°-45°-90°. Its side lengths have the ratios 1 : 1 : √2.
These triangles are useful to remember. They can help you remember the "short table of trig functions" (attached).
If you want to solve this using trig functions, you can use ...
Tan = Opposite/Adjacent
tan(60°) = 9√3/x
x = (9√3)/tan(60°) = (9√3)/(√3) = 9
and
Sin = Opposite/Hypotenuse
sin(60°) = 9√3/y
y = (9√3)/sin(60°) = (9√3)/(√3/2) = 18