Question

PLEASE HELP

Which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle? Check all that apply.

Answer 1

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. So, in this case our numbers are the two legs of a triangle. Given that this is a right triangle because one angle is equal to 90, the the relations are as follows:


`opposite=(hypotenuse)(sin\alpha)`

`adjacent=(hypotenuse)(cos \alpha)`

In the figure below α = 30, so


`O=Hsin(30)`

`A=Hcos(30)`

There are two ratios:


`(O)/(A)` and


`(A)/(O)`

Therefore:


`(O)/(A)=(\sin(30))/(cos(30))=(√(3))/(3)=(1)/(√(3))`


`(A)/(O)=(\cos(30))/(sin(30))=√(3)`

Finally, matching these results with the image above, the ratio:


`1: √(3) = (1)/( √(3) )`

is the only one that apply