SOLUTION: What is the legnth of the hypotenuse of a 30-60-90 triangle whose longer leg has a length of 6 radical 3 ft?

Question 617680: What is the legnth of the hypotenuse of a 30-60-90 triangle whose longer leg has a length of 6 radical 3 ft?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
SHORT ANSWER:
The fastest way to write an answer seems to be invoking trigonometric ratios.
The long leg is opposite the angle, so
-->
long_leg=
and
Putting it al together

HOW WE KNOW THOSE TRIGONOMETRIC RATIOS:
A 30-60-90 triangle is half of an equilateral triangle:

, so (The hypotenuse is twice as long as the short leg).
Using the Pythagorean theorem (), we get
--> --> --> --> -->
So the trigonometric ratios in a 30-60-90 triangle are

RELATED QUESTIONS
find the measure of the hypotenuse of a 30-60-90 triangle whose longer leg has a measure... (answered by nerdybill)

Find the measure of the hypotenuse of a 30-60-90 triangle whose longer leg has a measure... (answered by edjones)

In a 30-60-90 triangle the longer leg has length of 7 what is the length of the... (answered by josgarithmetic,ikleyn,MathTherapy)

If the longer leg of a 30, -60, -90 degree triangle is 6, what is the length of the... (answered by scott8148)

The hypotenuse of a 30-60-90 triangle measures 6 in. What is the length of the longer... (answered by Alan3354)

If the hypotenuse of a 30�60�90 triangle has length meters, what is the length of the... (answered by stanbon)

What is the length of the longer leg of a 30-60-90 triangle with a hypotenuse of length... (answered by richwmiller)

The shortest leg of a 30, 60, 90 triangle has a length of 6. What is the length of the... (answered by josgarithmetic)

Find the longer leg of a 30-60-90 triangle if its hypotenuse is... (answered by Theo,MathTherapy)