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The length of the hypotenuse of a 30 degrees -60 degrees 90 degrees triangle is 9. What is the perimeter?
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The length of the hypotenuse of a 30 degrees -60 degrees 90 degrees triangle is 9. What is the perimeter?
27/2 + 9/2 3
9/2 + 27/2 3
9 + 27 3
27 + 9 3
27/2 + 9/2 3
9/2 + 27/2 3
9 + 27 3
27 + 9 3
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The 30-60-90 triangle has a special relationship between its sides. The hypotenuse is twice as long as the shorter leg (opposite the 30 degree angle) and the longer leg (opposite the 60 degree angle) is the square root of three times the shorter leg.
In this problem, we know the hypotenuse is 9, so the shorter leg (opposite the 30 degree angle) is 9/2. The longer leg (opposite the 60 degree angle) is (sqrt(3))(9/2) = (9/2)sqrt(3).
To find the perimeter, we add up the lengths of all three sides:
Perimeter = (9/2) + (9/2)sqrt(3) + 9
Simplifying, we can factor out a common factor of (9/2) to get:
Perimeter = (9/2)(1 + sqrt(3) + 4)
Perimeter = (9/2)(5 + sqrt(3))
Perimeter ≈ 23.4
Therefore, the perimeter is approximately 23.4.
In this problem, we know the hypotenuse is 9, so the shorter leg (opposite the 30 degree angle) is 9/2. The longer leg (opposite the 60 degree angle) is (sqrt(3))(9/2) = (9/2)sqrt(3).
To find the perimeter, we add up the lengths of all three sides:
Perimeter = (9/2) + (9/2)sqrt(3) + 9
Simplifying, we can factor out a common factor of (9/2) to get:
Perimeter = (9/2)(1 + sqrt(3) + 4)
Perimeter = (9/2)(5 + sqrt(3))
Perimeter ≈ 23.4
Therefore, the perimeter is approximately 23.4.
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Sure! A 30-60-90 triangle is a special type of right triangle in which the measures of the angles are always 30 degrees, 60 degrees, and 90 degrees.
The relationship between the sides of a 30-60-90 triangle is always the same:
- The side opposite the 30 degree angle (the shorter leg) is half the length of the hypotenuse.
- The side opposite the 60 degree angle (the longer leg) is (sqrt(3)) times as long as the shorter leg.
- The hypotenuse is always twice as long as the shorter leg.
In this problem, we are given the length of the hypotenuse as 9. We can use the formulae above to find the lengths of the other sides.
Since the hypotenuse is twice as long as the shorter leg, we can divide 9 by 2 to find that the shorter leg is 4.5.
Since the longer leg is (sqrt(3)) times as long as the shorter leg, we can multiply 4.5 by (sqrt(3)) to find that the longer leg is (4.5)(sqrt(3)) = (9/2)(sqrt(3)).
Now that we know the lengths of all three sides, we can add them together to find the perimeter, which is:
Perimeter = (shorter leg) + (longer leg) + (hypotenuse)
Perimeter = 4.5 + (9/2)sqrt(3) + 9
Perimeter = (9/2) + (9/2)sqrt(3) + 9
Perimeter = (9/2)(1 + sqrt(3) + 4)
Perimeter = (9/2)(5 + sqrt(3))
Perimeter ≈ 23.4
Therefore, the perimeter is approximately 23.4.
The relationship between the sides of a 30-60-90 triangle is always the same:
- The side opposite the 30 degree angle (the shorter leg) is half the length of the hypotenuse.
- The side opposite the 60 degree angle (the longer leg) is (sqrt(3)) times as long as the shorter leg.
- The hypotenuse is always twice as long as the shorter leg.
In this problem, we are given the length of the hypotenuse as 9. We can use the formulae above to find the lengths of the other sides.
Since the hypotenuse is twice as long as the shorter leg, we can divide 9 by 2 to find that the shorter leg is 4.5.
Since the longer leg is (sqrt(3)) times as long as the shorter leg, we can multiply 4.5 by (sqrt(3)) to find that the longer leg is (4.5)(sqrt(3)) = (9/2)(sqrt(3)).
Now that we know the lengths of all three sides, we can add them together to find the perimeter, which is:
Perimeter = (shorter leg) + (longer leg) + (hypotenuse)
Perimeter = 4.5 + (9/2)sqrt(3) + 9
Perimeter = (9/2) + (9/2)sqrt(3) + 9
Perimeter = (9/2)(1 + sqrt(3) + 4)
Perimeter = (9/2)(5 + sqrt(3))
Perimeter ≈ 23.4
Therefore, the perimeter is approximately 23.4.
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None of these answers is correct.
To solve this problem, we need to use the fact that in a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is (sqrt(3)) times the length of the shorter leg.
Since we are given the length of the hypotenuse as 9, we can divide by 2 to find the length of the shorter leg:
(shorter leg) = (hypotenuse) / 2 = 9 / 2 = 4.5
Then, we can use the fact that the longer leg is (sqrt(3)) times the length of the shorter leg to find its length:
(longer leg) = (sqrt(3)) x (shorter leg) = (sqrt(3)) x 4.5 = 4.5(sqrt(3))
Finally, we can find the perimeter by adding up the lengths of all three sides:
perimeter = (shorter leg) + (longer leg) + (hypotenuse)
perimeter = 4.5 + 4.5(sqrt(3)) + 9
perimeter = 13.5 + 4.5(sqrt(3))
Therefore, the perimeter of the triangle is 13.5 + 4.5(sqrt(3)).
To solve this problem, we need to use the fact that in a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is (sqrt(3)) times the length of the shorter leg.
Since we are given the length of the hypotenuse as 9, we can divide by 2 to find the length of the shorter leg:
(shorter leg) = (hypotenuse) / 2 = 9 / 2 = 4.5
Then, we can use the fact that the longer leg is (sqrt(3)) times the length of the shorter leg to find its length:
(longer leg) = (sqrt(3)) x (shorter leg) = (sqrt(3)) x 4.5 = 4.5(sqrt(3))
Finally, we can find the perimeter by adding up the lengths of all three sides:
perimeter = (shorter leg) + (longer leg) + (hypotenuse)
perimeter = 4.5 + 4.5(sqrt(3)) + 9
perimeter = 13.5 + 4.5(sqrt(3))
Therefore, the perimeter of the triangle is 13.5 + 4.5(sqrt(3)).
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