What is the length of the longer leg of a 30 60 90 triangle with a hypotenuse of length 12 square root 3?

Question

What is the length of the longer leg of a 30 60 90 triangle with a hypotenuse of length 12 square root 3?

Answer 1

Student would be well advised to memorize the basic ratio of sides, which is 1:√3:2, these sides being

short leg longer leg and hypotenuse, respectively.

 

All problems of this type can be solved using proportions based on similarity of all 30-60-90 triangles.

Answer 2

the side opposite the 30º angle is half of the hypotenuse

this side is (1/2)(12√3)=6√3

the longer side is the shorter side times √3

6√3*√3=18

check: 18^2+(6√3)^2=(12√3)^2

324+108=432

432=432