They are described by the famous Pythagoras theorem, if "a" and "b" are the legs and "h" the hypotenuse, then
h x h = (a x a) + (b x b)
Also a = h x sinB (where B is the internal angle (of the triangle) between the hypotenuse and side b
and
b = h x sinA (where A is the internal angle (of the triangle) between the hypotenuse and side a
The hypotenuse is the side opposite to the right angle in the triangle.
The short leg is equal to one-half of the hypotenuse. ( sin 30 = opposite/hypotenuse = short leg/hypotenuse = 1/2)
The two legs squared and added together = the length of the hypotenuse's length squared
right triangle
The longer leg is square root of 3 bigger than the short leg. That is because sin 30 = 1/2 = short/hypotenuse; cos 30 = long/hypotenuse = (sqrt 3)/2
The hypotenuse is the side opposite to the right angle in the triangle.
The short leg is equal to one-half of the hypotenuse. ( sin 30 = opposite/hypotenuse = short leg/hypotenuse = 1/2)
The square of the two legs is equal to the square of the hypotenuse. a2+b2 = c2 where a and b are the legs and c being the hypotenuse
Both legs are equal in length
hypotenuse, hypotenuse
The two legs squared and added together = the length of the hypotenuse's length squared
right triangle
As the relationship between the length and angle given are unclear a graphic explanation can be found at the link below
Ah, what a lovely question we have here. In a right triangle, the ratio of the adjacent side to the hypotenuse is called cosine. It helps us understand the relationship between the lengths of the sides and the angles of the triangle. Just remember, happy little ratios like these can help you create beautiful mathematical landscapes on your canvas of knowledge.
The longer leg is square root of 3 bigger than the short leg. That is because sin 30 = 1/2 = short/hypotenuse; cos 30 = long/hypotenuse = (sqrt 3)/2
To find the hypotenuse of a non-right triangle, you can use the Law of Cosines. This theorem states that the square of the length of one side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the angle between them. By rearranging the formula and plugging in the known side lengths and angles, you can solve for the length of the hypotenuse.
There is the Pythagorean relationship between the side lengths. Given a right triangle with sides a, b, & c : Sides a & b are adjacent to the right angle, and side c is opposite the right angle, and this side is called the hypotenuse. Side c is always the longest side, and can be found by c2 = a2 + b2 The 2 angles (which are not the right angle) will add up to 90° Given one of those angles (call it A), then sin(A) = (opposite)/(hypotenuse) {which is the length of the side opposite of angle A, divided by the length of the hypotenuse} cos(A) = (adjacent)/(hypotenuse), and tan(A) = (opposite)/(adjacent).