Answer:
A. √3 : 2
D. 3√3 : 6
Step-by-step explanation:
In a triangle described as 30°-60°-90° triangle, the base angles are 90° and 60°
The side with angles 90° and 60° is the shortest leg and can be represented by 1 unit
The hypotenuse side is assigned a value twice the shorter leg value, which is 2 units
From Pythagorean relationship; the square of the hypotenuse side subtract the square of the shorter leg gives the square of the longer side
This is to say if;
The given the shorter leg = 1 unit
The hypotenuse is twice the shorter leg= 2 units
The longer leg is square-root of the difference between the square of the hypotenuse and that of the shorter leg
[tex]=2^2-1^2\\\\=4-1=3\\\\\\b^2=3\\\\\\b=\sqrt{3}[/tex]
where the longer leg is represented by side b in the Pythagorean theorem, the hypotenuse by c and the shorter leg by a to make;
[tex]a^2+b^2=c^2[/tex]
Hence the summary is
a=shorter leg= 1 unit
b=longer leg = √3 units
c=hypotenuse=2 units
The ratio of longer leg to its hypotenuse is
=√3:2⇒ answer option A
This is the same as 3√3:6 ⇒answer option D because you can divide both sides of the ratio expression by 3 and get option A
[tex]=3\sqrt{3} :6\\\\\\\frac{3\sqrt{3} }{3} :\frac{6}{3} \\\\\\=\sqrt{3} :2[/tex]
Answers are :option A and D
