Why is Pythagorean theorem important?

Why is Pythagorean theorem important?

The Pythagorean Theorem is useful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. The distances north and west will be the two legs of the triangle, and the shortest line connecting them will be the diagonal. The same principles can be used for air navigation.

How is the Pythagorean theorem used in construction?

Architects use the Pythagorean Theorem to calculate the heights of buildings and the lengths of walls. Athletes even use the Pythagorean Theorem when they are calculating distances, which are important in determining how fast they can run or where a ball needs to be thrown.

What is interesting about the Pythagorean Theorem?

In mathematics, the Pythagorean theorem or Pythagoras’s theorem is a statement about the sides of a right triangle. One of the angles of a right triangle is always equal to 90 degrees. The hypotenuse is the side opposite to the right angle, and it is always the longest side. It was discovered by Vasudha Arora.

How do we use Pythagoras theorem in daily life?

The Pythagorean Theorem is useful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. … The distances north and west will be the two legs of the triangle, and the shortest line connecting them will be the diagonal. The same principles can be used for air navigation.

Does 9 12 15 make a right triangle?

The three sides 9 in, 12 in, and 15 in do represent a right triangle. Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, this is a right triangle.

Does 20 25 and 15 represent a right triangle?

The largest length is always the hypotenuse. If we were to multiply any triple by a constant, this new triple would still represent sides of a right triangle. Therefore, 6, 8, 10 and 15, 20, 25, among countless others, would represent sides of a right triangle.

Does 20 21 and 29 make a right triangle?

. The right triangle having these side lengths is sometimes called the 3, 4, 5 triangle. One side may have two of these divisors, as in (8, 15, 17), (7, 24, 25), and (20, 21, 29), or even all three, as in (11, 60, 61). …

Does 5 12 and 13 form a right triangle?

Yes, a right triangle can have side lengths 5, 12, and 13. To determine if sides of length 5, 12, and 13 units can make up the sides of a right…

Does 28 53 45 form a right triangle?

53 is the greatest side.So, it must be a hypotenuse. adjacent and opposite are nothing but the sides other than hypotenuse(=53) i.e,28 and 45. It is obeying the pythagoras theorem then by the converse of pythagoras theorem it is a right triangle.

Does 4 8 12 make right triangles?

Answer: No, side lengths of 4, 8, and 12 do not form a right triangle.

Does 12 16 and 20 make a right triangle?

So we type GCF(12,16,20) and we get 4. And lo and behold, we get a Pythagorean Triple of 3, 4, 5. So yes, this is a right triangle.

How do you solve special right triangles?

Step 1: This is a right triangle with two equal sides so it must be a 45°-45°-90° triangle. Step 2: You are given that the both the sides are 3. If the first and second value of the ratio x:x:x√2 is 3 then the length of the third side is 3√2. Answer: The length of the hypotenuse is 3√2 inches.

Does 10 24 26 Make a right triangle?

Answer Expert Verified Yes. For right triangles, the sum of the squares of the shorter sides is equal to the square of the longer side. Thus, this is a right triangle if 10^2+24^2=26^2. Expanding these squares, we have which is true.

Does 6 8 and 10 make a right triangle?

Answer: Yes, a triangle has side lengths 6, 8, 10 is it a right triangle.

Does 12 35 37 Make a right triangle?

If this is a right triangle we can then substitute the sides of the triangle (12 and 35) and the hypotenuse (37) into the Pythagoras Theorem and the two sides of the equation will be equal. If this is not a right triangle the two sides of the equation will not be equal. Because these are equal this is a right triangle.

Does 5 6 7 make right triangles?

Therefore in this problem 7 is the larger length and should be the hypotenuse, and 5 and 6 should be the lengths of the other two sides. If the sum of the squares of the 2 legs of a triangle is equal to the square of the triangle’s hypotenuse, then the triangle is a right triangle.

Does 9 40 41 make a right triangle?

Yes, 9, 40, 41 is a Pythagorean Triple and sides of a right triangle.

Does 30 40 45 Make a right triangle?

Explanation: Pythagoras’s Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. Actually a 30 , 40 , 50 triangle is just a scaled up 3 , 4 , 5 triangle, which is a well known right angled triangle.

Why is it not possible to make a right triangle using lengths of 10 feet 60 feet and 65 feet?

7. Why is it not possible to make a right triangle using lengths of 10 feet, 60 feet, and 65 feet? A 10+ 60 is greater than 65. The lot is 72 feet long.

Does 7 10 12 make a right triangle?

The triangle that has side lengths of 7, 10, and 12 is not a right triangle. The correct answer is B.

Does 7.5/10 and 12.5 make a right triangle?

A triangle with sides 7.5, 10, and 12.5 is a right triangle.

Does 15 36 39 Make a right triangle?

Example 1: Solve for x. Therefore, the length of the base x of the triangle is approximately 12.1. The Converse of the Pythagorean Theorem states that, if is true, then the given triangle is a right triangle. Hence, the set {15, 36, 39} is a Pythagorean Triple.

Does 16 30 34 form a right triangle?

Solve for the missing side. Solve for the missing side. If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. Given the sides of a triangle equal to 16, 30, 34.

What are the side lengths of a 30 60 90?

A 30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º. The triangle is special because its side lengths are always in the ratio of 1: √3:2. Any triangle of the form 30-60-90 can be solved without applying long-step methods such as the Pythagorean Theorem and trigonometric functions.

What are the 5 most common Pythagorean triples?

Examples

(3, 4, 5)	(5, 12, 13)	(7, 24, 25)
(20, 21, 29)	(12, 35, 37)	(28, 45, 53)
(11, 60, 61)	(16, 63, 65)	(48, 55, 73)
(13, 84, 85)	(36, 77, 85)	(65, 72, 97)

Which is the length of the third side of the right triangle?

The side opposite the right angle is the hypotenuse. The Pythagorean theorem is used to solve for the length of the hypotenuse. If a right triangle has legs measuring a and b with hypotenuse c, the Pythagorean theorem is a² + b² = c².