By using 30-60-90 Special Triangle, sides are computed always as,
shortest side = a
longest side or hypotenuse = 2a
middle side = a√3
see attached picture for additional information.
#1.
shortest side = a = 6
longest side or hypotenuse = 2a = 12
middle side = a√3 = x
solve for x
x = a√3
but a = 6
so,
x = 6√3
alternativel solution, use Pythagorean Theorem,
c² = a² + b²
12² = 6² + x²
x² = 144 - 36
x = √108
x = √(36)(3)
#2.
shortest side = a = y
longest side or hypotenuse = 2a = 20√3
solve for a,
2a = 20√3
a = (20√3) / 2
a = 10 √3
solve for x,
but a = 10 √3
x = (10 √3) (√3)
x = 10 (3)
x = 30
solve for y,
y = a
y = 10 √3
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Answers & Comments
By using 30-60-90 Special Triangle, sides are computed always as,
shortest side = a
longest side or hypotenuse = 2a
middle side = a√3
see attached picture for additional information.
SOLUTION:
#1.
shortest side = a = 6
longest side or hypotenuse = 2a = 12
middle side = a√3 = x
solve for x
x = a√3
but a = 6
so,
x = 6√3
so answer is x = 6√3
alternativel solution, use Pythagorean Theorem,
c² = a² + b²
12² = 6² + x²
x² = 144 - 36
x = √108
x = √(36)(3)
x = 6√3
#2.
shortest side = a = y
longest side or hypotenuse = 2a = 20√3
middle side = a√3 = x
solve for a,
2a = 20√3
a = (20√3) / 2
a = 10 √3
solve for x,
x = a√3
but a = 10 √3
so,
x = (10 √3) (√3)
x = 10 (3)
x = 30
solve for y,
y = a
but a = 10 √3
so,
y = 10 √3
therefore,
x = 30
y = 10 √3
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PYTHAGOREAN THEOREM
Solutions and Answers for #1:
Solutions and Answers for #2:
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