Question

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse? check all that apply

3:2/3
1:/3
/3:2
3 /3:6
/2:/3
/3:/3

Answer 1

we are asked to determine the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse. we can find this out using a calculator preferably in the degrees mode. When hypotenuse is 1, the longer leg measure sqrt 3 over 2. when hypotenuse is 2, the longer leg measure sqrt 3. hence the answer is C>

Answer 2

we know that

in a
`30-60-90` triangle

`sin(30\°)=cos(60\°)=(1)/(2)`

`sin(60\°)=cos(30\°)=(√(3))/(2)`

`(√(3))/(2) > (1)/(2)`

so

the ratio of the length of the longer leg to the length of its hypotenuse is equal to
`(√(3))/(2)`

therefore

the answer is the option

`√(3):2`