SOLUTION: if one leg of a 30, 60 ,90 degree triangle has a length of 6 and the adjacent angel is 30 , what is the exact length of the hypotenuse in simplest radical form

Question 616924: if one leg of a 30, 60 ,90 degree triangle has a length of 6 and the adjacent angel is 30 , what is the exact length of the hypotenuse in simplest radical form
Found 3 solutions by dragonwalker, josmiceli, solver91311:
Answer by dragonwalker(73)   (Show Source): You can put this solution on YOUR website!
As it has an angle that is 90 degrees it is a right-angle triangle and therefore cosine, sine and tangent can be used to find the angles.
As the side that is 6 long is adjacent to the known angle of 30 you can use cosine:
(Cosine (angle) = adjacent/hypotenuse
so:
Cos 30 = 6/h where h is the unknown hypotenuse.
reaarange by moving the h to the other side by multiplying both sides by h:
Cos 30 x h = 6
and then move the Cos 30 by dividing both sides by Cos 30:
h = 6/ Cos 30
now calculate using the cos function:
h = 6.93

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The sides are in these ratios:
Side opposite 30 degree angle:
Side opposite 60 degree angle:
Side opposite 90 degree angle:
----------
The side adjacent to the 30 degree angle is
opposite the 60 degree angle
Figure out the new ratios

----------
So the lengths are:

The length of the hypotenuse is
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

If you have a question that involves an "angel", adjacent or otherwise, please ask the local clergyperson or tribal shaman of your personal choice. In the event you actually meant "angle", read on:

The short leg of a 30-60-90 right triangle always measures one-half the measure of the hypotenuse. C.f. .

So if you have a right triangle where one leg measures 6, another leg measures and the hypotenuse measures , then, according to Mr. Pythagoras:

Solve for .

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
If the longer leg of a 30, -60, -90 degree triangle is 6, what is the length of the... (answered by scott8148)
The shortest leg of a 30, 60, 90 triangle has a length of 6. What is the length of the... (answered by josgarithmetic)
if the shortest leg of a 30-60-90 triangle has length 7, the length of the hypotenuse... (answered by ewatrrr)
In a 30-60-90 triangle the longer leg has length of 7 what is the length of the... (answered by josgarithmetic,ikleyn,MathTherapy)
A 30-60-90 triangle has a long leg of length 22. What is the area of this right... (answered by edjones)
If the hypotenuse of a 30�60�90 triangle has length meters, what is the length of the... (answered by stanbon)
Given a 30-60-90 triangle. The length of the longer leg is 4root2. What is the length of... (answered by VFBundy)
The hypotenuse of a 30-60-90 triangle measures 6 in. What is the length of the longer... (answered by Alan3354)
in a 30 dgree -60 and -90 degree triangle , if the shoter leg is p, than the longer leg... (answered by Alan3354)