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
In a 30° 60° 90° triangle, the ratio (long leg)/hypotenuse = sqrt(3)/2 ~ 0.866The ratio (short leg)/hypotenuse = 1/2 = 0.5
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.
No.
Each leg is 21.73 feet and the Hypotenuse is 30.73 feet. (0.73 feet is a whisker over 8¾ inches)
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
23
7.44 - 7.45
In a 30° 60° 90° triangle, the ratio (long leg)/hypotenuse = sqrt(3)/2 ~ 0.866The ratio (short leg)/hypotenuse = 1/2 = 0.5
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.
1/2 sqrt(3) = 0.866 (rounded)
2 Square Root 3 And 4
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.
1/2 sqrt(3) = 0.866 (rounded)
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.
The hypotenuse must be longer than the other other leg.
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.
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.