Question 1172290: Please check my work, thank you.
2. A 30-60-90 triangle has a hypotenuse of 10. Use special right triangle formulas to find the long side. Explain your work.
Hypotenuse = x : x√3 : 2x
Hyp - 5 x 2 = 10
Longest leg is 5 (square rt3) which will be 8.660
Long side = 8.660
Found 3 solutions by Boreal, Edwin McCravy, MathTherapy:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! You are correct, except for the 5*2 =10 part. The shortest side (which they aren't asking for) is 1/2 of the hypotenuse. If they want the exact solution, keep the radical and 5 sqrt(3).
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
Here's what you're supposed to do. For this problem you aren't supposed to do
any calculations at all. You are to start by drawing the special 30-60-90
right triangle that you should memorize. Learn how it looks when it's standing
up or when it's lying down. Learn the sides. The shortest side (leg) is 1, the
middle size side (leg) is √3 and the longest (the hypotenuse) is 2. The
smallest angle is 30°, the middle-sized angle is 60° and the right angle is, of
course, 90°.
Then since your problem says a 30-60-90 triangle has a hypotenuse of 10,
instead of the sides being
 ,
 ,
 ,
as they are for the standard 30-60-90 right triangle,
since 10 is the hypotenuse, you just multiply all three sides
by 5 and get:
 ,
 ,
Edwin
Answer by MathTherapy(10552)  (Show Source):
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