Q: 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?

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No. Due to Pythagoras' Theorem, the square of the hypotenuse (the longest side of the right triangle) has to be equal to the sum of the squares of the other two sides. If this is too wordy, call the sides a, b and c, where c is the hypotenuse. Then a2+b2=c2 for any right triangle. Hence, with 3, 6 and 8 we have 9+36=64 (or 36+9=64 depending on how you choose a and b) which is clearly wrong, so a triangle with sides of length 3, 6 and 8 is NOT a right triangle.

No. The hypotenuse is the side of a right triangle that is not adjacent to the right angle. The Pythagorean theorem says that a2+b2=h2 where h is the length of the hypotenuse and a and b are the lengths of the other sides. Let's say the hypotnuse is 3, then a2+b2=9 a and b could be the 1 and the square root of 8 or the square root of 2 and the square root of 7 or the square root of 3 and the square root of 6. In fact, there are an infinite number of combinations of lengths that a and b could be.

The way you can work out the length of a triangle is if you are given the height and the area of that triangle ( this works of you don't want to measure it) or you could just measure it.

They could all be the same length, or two of them could be the same, or they could all be different. In any case, when you add them all up, the number you get is called the "perimeter" of the triangle.

Without a type of triangle and the associated angle measurements, an answer is impossible.

Related questions

2 Square Root 3 And 4

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

In such a triangle, the sides will always be in the ratio, 1, 2 (hypotenuse) and sqrt(3) So the ratio you want is sqrt(3)/2

There's no such thing as the "length of a 30-60-90". The ratios of the lengths of the legs of such a triangle to the length of the hypotenuse are 1/2 and 1/2(sqrt(3).

Assuming that 30-60-90 refers to the angles (in degrees), the ratio of the longer leg to the hypotenuse would be 1:cosine(30) = 1:sqrt(3)/2 or 2:sqrt(3)

Or course. 1 & sq. rt. of 3 being the sides, 2 being the hypotenuse.

No. Due to Pythagoras' Theorem, the square of the hypotenuse (the longest side of the right triangle) has to be equal to the sum of the squares of the other two sides. If this is too wordy, call the sides a, b and c, where c is the hypotenuse. Then a2+b2=c2 for any right triangle. Hence, with 3, 6 and 8 we have 9+36=64 (or 36+9=64 depending on how you choose a and b) which is clearly wrong, so a triangle with sides of length 3, 6 and 8 is NOT a right triangle.

If all you're given is the hypotenuse, then you can't figure out any more information. If you had the length of one more side you could use Pythagoras's Theorem a2+ b2= c2to find the other side, or if you were given an angle other than the right angle, you could use SOH CAH TOA to calculate the length of another side. With just the hypotenuse, nothing more can be found.

Any value between 7 and 17------------------------------------To create a triangle, the sum of the two shorter sides must be greater than the third side.If the side of length 12 is the longer side then the missing side must be greater than 12 - 5 = 7If the missing side is the longer side then the missing side must be less than 5 + 12 = 17Thus any length that is greater than 7 and less than 17.-----------------------------------------------------------------------A Pythagorean triangle would have a hypotenuse of 13

Not enough information. If it's a right triangle, and the missing side is a leg, it could be 4 in. If the missing side is the hypotenuse, it would be the square root of 34.

No. The hypotenuse is the side of a right triangle that is not adjacent to the right angle. The Pythagorean theorem says that a2+b2=h2 where h is the length of the hypotenuse and a and b are the lengths of the other sides. Let's say the hypotnuse is 3, then a2+b2=9 a and b could be the 1 and the square root of 8 or the square root of 2 and the square root of 7 or the square root of 3 and the square root of 6. In fact, there are an infinite number of combinations of lengths that a and b could be.

Without knowing the measurement of one of its legs it's impossible to work out using Pythagoras' theorem. So from an experienced guess the two legs could be 8 cm and 6 cm with an hypotenuse of 10 cm.