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

Algebra ->  Triangles -> 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      Log On


   

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) About Me  (Show Source):
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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) About Me  (Show Source):
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The sides are in these ratios:
Side opposite 30 degree angle: +1+
Side opposite 60 degree angle: +sqrt%283%29+
Side opposite 90 degree angle: +2+
----------
The side adjacent to the 30 degree angle is
opposite the 60 degree angle
Figure out the new ratios
+1%2Fsqrt%283%29+=+x%2F6+
+x+=+6%2Fsqrt%283%29+
+x+=+2%2Asqrt%283%29+
----------
So the lengths are:
+2%2Asqrt%283%29+
+6+
+4%2Asqrt%283%29+
The length of the hypotenuse is +4%2Asqrt%283%29+

Answer by solver91311(24713) About Me  (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
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