contestada

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

Respuesta :

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>

calculista

we know that

in a [tex]30-60-90[/tex] triangle

[tex]sin(30\°)=cos(60\°)=\frac{1}{2}[/tex]

[tex]sin(60\°)=cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\sqrt{3}}{2} > \frac{1}{2}[/tex]

so

the ratio of the length of the longer leg to the length of its hypotenuse is equal to [tex]\frac{\sqrt{3}}{2}[/tex]

therefore

the answer is the option

[tex]\sqrt{3}:2[/tex]