What is the length of the hypotenuse of a right triangle with legs of length 21 ft and 72 ft?

Explanation: By the Pythagorean Theorem, 212 + 722 = hyp2. Then hyp2 = 5625, and the hypotenuse = 75.

What is the hypotenuse of the given triangle?

In a right triangle, the hypotenuse is the longest side, an “opposite” side is the one across from a given angle, and an “adjacent” side is next to a given angle. We use special words to describe the sides of right triangles. The hypotenuse of a right triangle is always the side opposite the right angle.

How do you find the sides of a triangle with hypotenuse?

If you have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle. Alternatively, multiply the hypotenuse by cos(θ) to get the side adjacent to the angle.

How do you calculate the hypotenuse?

The hypotenuse is termed as the longest side of a right-angled triangle. To find the longest side we use the hypotenuse formula that can be easily driven from the Pythagoras theorem, (Hypotenuse)2 = (Base)2 + (Altitude)2. Hypotenuse formula = √((base)2 + (height)2) (or) c = √(a2 + b2).

How do you find the hypotenuse of a triangle with one leg?

Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²) Given angle and one leg. c = a / sin(α) = b / sin(β), from the law of sines. Given area and one leg.

What is the sum of the length of the hypotenuse?

The sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse . Usually, this theorem is expressed as A 2 + B 2 = C 2 . SOHCAHTOA only applies to right triangles ( more here) . The hypotenuse is the largest side in a right triangle and is always opposite the right angle.

What is the sum of the squares of the right triangles?

A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.

Can the Pythagorean theorem be represented in terms of area?

The Pythagorean Theorem can also be represented in terms of area. In any right triangle, the area of the square drawn from the hypotenuse is equal to the sum of the areas of the squares that are drawn from the two legs. You can see this illustrated below in the same 3-4-5 right triangle.