The area of a right triangle is 32sqrt(3). One of the acute angles is 30^(circ). Find the length of the hypotenuse

Terry Briggs 2022-09-14 Answered
The area of a right triangle is 32 3 . One of the acute angles is 30 . Find the length of the hypotenuse.
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Answers (1)

ignaciopastorp6
Answered 2022-09-15 Author has 14 answers
a, b --- legs
c --- hypotenuse
c = 2a --- the leg against an angle of 30 degrees is equal to half the hypotenuse
S = 0.5 a b = 32 3
a b = 64 3
c 2 = a 2 + b 2
4 a 2 = a 2 + ( 64 3 / a ) 2
3 a 2 = 64 2 3 / a 2
a 4 = 64 2
a 2 = 64
a = 8
c = 16

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