Answer:
D)16
Step-by-step explanation
we are given a 30-60-90 triangle and the longer side of the triangle
remember the properties of 30-60-90 triangle
- the hypotenuse is twice as much as the shorter leg
- the longer leg is the square root of 3 times shorter leg
as we are given the longer leg we'll use the second property
let the shorter leg be x
so our equation is
[tex]\displaystyle x\sqrt{3}=16\sqrt{3}[/tex]
divide both sides by √3:
[tex]\displaystyle \frac{x\sqrt{3}}{\sqrt{3}}=\frac{16\sqrt{3}}{\sqrt{3}}[/tex]
[tex]\displaystyle x=16[/tex]
hence,
the length of the shorter leg is 16
