SOLUTION: Find the remaining sides of a 30°-60°-90° triangle if the longest side is 11. (Enter your answers as a comma-separated list.)

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Question 1080068: Find the remaining sides of a 30°-60°-90° triangle if the longest side is 11. (Enter your answers as a comma-separated list.)
Found 3 solutions by Alan3354, MathLover1, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the remaining sides of a 30°-60°-90° triangle if the longest side is 11.
If by "longest side" you mean the hypotenuse:
Shortest side = 11*sin(30) = 5.5
Other side = sqrt%2811%5E2+-+5.5%5E2%29
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(Enter your answers as a comma-separated list.)
Enter them any way you like.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The triangle is significant because the sides exist in an easy-to-remember ratio:
1:sqrt%283%29:2
That is to say, the hypotenuse is twice as long as the shorter%7B%7B%7B+leg,
and the+longer+leg is the sqrt%283%29 times the shorter leg.
so, if the longest side is 11, means the hypotenuse c is 11
if the hypotenuse is twice as long as the shorter+leg b, than b=11%2F2=5.5
and the+longer+leg a is the sqrt%283%29 times the shorter leg :sqrt%283%29%2A5.5=9.526279441628825=9.5
solution:
5.5,9.5,11



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find the remaining sides of a 30°-60°-90° triangle if the longest side is 11. (Enter your answers as a comma-separated list.)
The HYPOTENUSE is the longest side
Shorter LEG: highlight_green%28HYPOTENUSE%2F2%29
Longer LEG: