Question

Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form

Answer 1

The ratio of a 30-60-90 triangle is the following:

This means that the side that is opposite to the 60 degrees angle is "a" times the square root of 3, where "a" is the side adjacent to the 60 degrees angle. Therefore, applying this to the given triangle we get:

`m=n\sqrt[]{3}`

Also, the hypotenuse is "2a", therefore, we have:

`84=2(n)`

From there we can solve for "n" by dividing both sides by 2:

`n=(84)/(2)=42`

Now we can use this value to determine the value of "m":

`m=42\sqrt[]{3}`