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Starting with an equilateral triangle of side 2, dropping a perpendicular from one vertex to the opposite base creates two equal right angled triangles with hypotenuse of length 2, base length 1 and height of length √(22 - 12) = √3 which is the longer leg of the 30-60-90 triangle.

Thus the ratio of longer_leg : hypotenuse is √3 : 2

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Q: The ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?
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What could be the ratio of the length of of the longer leg of a 30 60 90 triangle to the length of its hypotenuse?

In a 30° 60° 90° triangle, the ratio (long leg)/hypotenuse = sqrt(3)/2 ~ 0.866The ratio (short leg)/hypotenuse = 1/2 = 0.5


How do you find the length of the sides of a right triangle when you know the hypotenuse?

If it is a 45-45-90 triangle, then divide the hypotenuse by the square root of 2. If it is a 30-60-90 triangle, then the shorter leg would be the hypotenuse divided by 2. And the longer leg would be the the shorter leg multiplied by the square root of 3.


Can a leg of a right triangle be longer than the hypotenuse?

No.


The hypotenuse of an isosceles right triangle is 9 feet longer than either of its legs. what the exact length of each side?

Each leg is 21.73 feet and the Hypotenuse is 30.73 feet. (0.73 feet is a whisker over 8¾ inches)


If the length of the longer side of a right triangle is 3 more than the length of the shorter side the length of the hypotenuse is 3 more than the length of the longer side find e length of each side?

You can plug those values in the pythagorean theorem and find the hypotenuse: h = ((h - 3)2 + (h - 6)2)1/2 ∴ h2 = h2 - 6h + 9 + h2 - 12h + 36 ∴ h2 = 2h2 - 18h + 45 ∴ h2 - 18h + 45 = 0 ∴ (h - 3)(h - 15) = 0 ∴ h = 3, 15 So the length of the hypotenuse will be either 3 or 15. It can't be 3 though, since that would make the other sides 0 and -3, which is impossible. The answer then is 15. The triangle has a hypotenuse of 15, and sides of 12 and 9

Related questions

What is the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?

23


A 30- 60- 90 triangle has a hypotenuse of length 8.6 What is the length of the longer of the two legs?

7.44 - 7.45


What could be the ratio of the length of of the longer leg of a 30 60 90 triangle to the length of its hypotenuse?

In a 30° 60° 90° triangle, the ratio (long leg)/hypotenuse = sqrt(3)/2 ~ 0.866The ratio (short leg)/hypotenuse = 1/2 = 0.5


He length of the longer leg of a right triangle is 3ft more than three times the length of the shorter leg. The length of the hypotenuse is 4ft more than three times the length of the shorter leg. Fin?

The length of the longer leg of a right triangle is 3ftmore than three times the length of the shorter leg. The length of the hypotenuse is 4ftmore than three times the length of the shorter leg. Find the side lengths of the triangle.


What is the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?

1/2 sqrt(3) = 0.866 (rounded)


What could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?

2 Square Root 3 And 4


Why is the hypotenuse?

The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is always longer than the other two sides of the triangle. This is because the length of the hypotenuse is determined by the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.


What could the ratio of the length of the longer leg of a 30 60 90 triangle to the length of its hypotenuse?

1/2 sqrt(3) = 0.866 (rounded)


How do you find the length of the sides of a right triangle when you know the hypotenuse?

If it is a 45-45-90 triangle, then divide the hypotenuse by the square root of 2. If it is a 30-60-90 triangle, then the shorter leg would be the hypotenuse divided by 2. And the longer leg would be the the shorter leg multiplied by the square root of 3.


A right triangle has a hypotenuse of 10 cm and one leg that measures 5 to the 3rd power what is the length to the other leg?

The hypotenuse must be longer than the other other leg.


In a 30-60-90 triangle if the shorter leg has length p then the longer leg has length and the hypotenuse has length?

Use the rule that the shortest leg has length p, the other leg has length 2p and the hypotenuse has length p*sqrt(3) Where sqrt(number) if the square root of the number.


What is the length of the shorter leg of a right triangle if the longer leg has a length of 45 and the hypotenuse has a length of 53?

Subtract the squared longer leg's squared length from the hypotenuse's square to obtain the squared shorter leg length. Then find the square root of that answer for your final answer. In other words: 53 squared minus 45 squared equals your squared answer.