SOLUTION: A 30- 60- 90 triangle has its longer leg of length 7.8. What is the length of the shorter of the two legs? If necessary, round your answer to two decimal places.

Algebra ->  Pythagorean-theorem -> SOLUTION: A 30- 60- 90 triangle has its longer leg of length 7.8. What is the length of the shorter of the two legs? If necessary, round your answer to two decimal places.       Log On


   

Question 294425: A 30- 60- 90 triangle has its longer leg of length 7.8. What is the length of the shorter of the two legs? If necessary, round your answer to two decimal places.
Found 2 solutions by Fombitz, richwmiller:
Answer by Fombitz(32388) About Me  (Show Source):
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From trigonometry,
sin%2830%29=y%2F7.8
where y is the shorter leg.
y=7.8%2Asin%2830%29=3.9
THe other leg is
x=7.8%2Acos%2830%29=6.75

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
In a 30 60 90 right triangle the sides are in the ratio 1:2:sqrt(3) with the hypotenuse as 2 the shorter leg as 1 and the longer leg as sqrt(3)
so 7.8/sqrt(3) should be the shorter leg which is 4.5033.