Hypotenuse formula

Hypotenuse Formula The hypotenuse formula is used in a right-angled triangle, to calculate the longest side that is called thehypotenuse.The hypotenuse is always the side that is opposite to the right angle in a right triangle. We use the Pythagoras theorem to find the hypotenuse, and thus the hypotenuse formula. What Is Hypotenuse Formula? Hypotenuse formula or the Pythagoras Theorem Here, • c = hypotenuse • a = height (a leg) • b = base (a leg) From Pythagoras theorem,(hypotenuse) 2= (base) 2+ (height) 2 If we take the square root on both sides, we get the formula of the hypotenuse. Hypotenuse formula =√((base) 2+ (height) 2) (or) c =√ (a 2+ b 2) Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps. Examples on Hypotenuse Formula Let us solve some interesting problems using the hypotenuse formula. Example 1: Using hypotenuse formula solve for the longest side of the given bread slice that is similar to a right-angle triangle. Its heightis 13units and its base is 5 units. Solution: To find: The longest side (hypotenuse) of the bread slice. Its height = 13 units. Its base = 5 units. By using thehypotenuse formula, hypotenuse formula =√ ((base) 2+ (height 2) =√(5 2+13 2) =√25+169 =√194 =13.98 Answer: The longest side of the bread slice = 13.928 units. Example 2: The hypotenuse of a right triangle is 5 units. Its base is 3 units. Find its height using the hypotenuse formula. Solution: To find: The height of the ...

home / geometry / triangle / hypotenuse Hypotenuse The The length of a side of a triangle corresponds to the size of the angle opposite the side. Since the hypotenuse of a right triangle is the longest side of the triangle, the 90° angle opposite it is also the largest angle of the right triangle. This also makes sense because the internal angles of a triangle sum to 180°. Since all triangles have 3 sides and 3 internal angles, it is impossible for a right triangle to have another angle that is greater than or equal to 90°, because the third angle would have to be 0° or have a negative angle measurement. How to find the hypotenuse of a right triangle The hypotenuse of a right triangle can be found using the or Example: Find the hypotenuse length of the triangle below. Given legs a = 15 and b = 20: c 2 = 15 2 + 20 2 c 2 = 625 c = 25 So, the hypotenuse length is 25. It is also possible to find the hypotenuse of a triangle given a side and an angle of the triangle, however this requires the use of trigonometry. Refer to the the following relationships can be used to find the various sides and angles of a right triangle: sin(A) = ; sin(B) = cos(A) = ; cos(B) = tan(A) = ; tan(B) = In the relationships above, A, B, and C are the angles of the triangle opposite the sides a, b, and c, respectively.

The mathematical term "hypotenuse" comes down through the ages to us from a Greek word whose origin meant "stretching under," and when you look at a right triangle, you can almost feel the tension in that longest side, the hypotenuse. The hypotenuse of a right triangle has some interesting properties and is useful in both geometry and trigonometry. What is a right triangle? A right triangle has the required three sides and three interior angles. One of its interior angles is a right angle, opposite the hypotenuse, with the other two sides - legs - meeting to form that right angle. In a right triangle a leg can also be called a cathetus (plural: catheti). The two legs are, by definition, two altitudes or heights of the right triangle; the third altitude can be constructed by striking a perpendicular line segment from the hypotenuse to the right angle. Hypotenuse formula Pythagoras was a Greek mathematician and philosopher who is still remembered for the Pythagorean Theorem, probably developed not by him but by the school of thought he created: The Pythagorean theorem 13 = c 13=c 13 = c That was neat and simple because we used a Trigonometry Just as the word "hypotenuse" is reserved for the longest side of right triangles, trigonometry is a word reserved for the special branch of mathematics dealing exclusively with the relationships between sides and angles of triangles. The word itself comes from Greek words meaning "triangle measure." The mathematical relationships betwee...

The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent). Once you progress, you will be given the hypotenuse and would be needed to find the opposite or the adjacent side (a or b). The Pythagorean theorem is a simple formula which uses the squared value of a and b; for example "a=3 and b=4, what is the value of c?" you square a (3^2=9=a) and b (4^2=16=b) and add the 2 values (9+16=25) to get to c. To complete the question, you have to square root c's value (square root of 25=5) because the formula says c^2 and not just c. Once you have done that, you can check your answer by squaring a,b and c to see if you have added and divided (Square-rooted) correctly. Hope this helps! 5:27 he said that in order to complete the equation you have to take the positive square root of both sides, which for 25 would equal 5. But what does that mean? How did he get 5 from 25? What did he do, what did he divide 25 by and why did he divide that and not another number? I will be waiting for a response thank you to those that reply, I will be very thankful because I know I would be taking time away from you just so you can answer my question. Thanks! A square root is a number that produces a specified quantity when multiplied by itself. It goes hand in hand with exponents and squares. 2 squared is 4, and the square root of 4 ...

This article was co-authored by There are wikiHow marks an article as reader-approved once it receives enough positive feedback. In this case, several readers have written to tell us that this article was helpful to them, earning it our reader-approved status. This article has been viewed 1,389,482 times. Make sure that your triangle is a right triangle. The Pythagorean Theorem only works on right triangles, and by definition only right triangles can have a hypotenuse. If your triangle contains one angle that is exactly 90 degrees, it is a right triangle and you can proceed. • Right angles are often notated in textbooks and on tests with a small square in the corner of the angle. This special mark means "90 degrees." Assign variables a, b, and c to the sides of your triangle. The variable "c" will always be assigned to the hypotenuse, or longest side. Choose one of the other sides to be a, and call the other side b (it doesn't matter which is which; the math will turn out the same). Then copy the lengths of a and b into the formula, according to the following example: • If your triangle has sides of 3 and 4, and you have assigned letters to those sides such that a = 3 and b = 4, then you should write your equation out as: 3 2 + 4 2 = c 2. Learn to recognize Pythagorean Triple Triangles. The side lengths of a Pythagorean triple are integers that fit the Pythagorean Theorem. These special triangles appear frequently in geometry text books and on standardized tests like the S...

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Rachel Mcconnell Rachel is a certified math teacher for grades 6-8. She graduated from the University of Kansas with a bachelors in Middle Math Education. She has taught middle school math for four years throughout Connecticut, Georgia and Italy. She has passed Praxis tests in math, curriculum, and special education. • Instructor A right triangle is a triangle, which is a closed shape with three sides, that has one 90 degree angle. A 90-degree angle is also called a right angle, therefore, the name right triangle. A right triangle has two legs that come together at the right angle, and a hypotenuse that is opposite the right angle. Since the two legs are at a right angle they are also perpendicular to each other. These are the characteristics that make up a right triangle. Right triangles can be identified with a box at their right angle. This box is the notation that the angle is exactly 90 degrees. A Right Triangle Imagine that you are standing in front of a tree. You are standing 10 feet away from the tree. You are looking at the very top of the tree. You see a huge, delicious plum hanging from one of the branches. This plum happens to be hanging 30 feet in the air. Thirty feet is a bit too high for you to simply reach up and grab the plum. What will help you to get to this delectable piece of fruit? You need a ladder. But what size ladder do you need? To figure this out, you can use math. If you drew out your situation, you would see that you, the tree, and the fruit f...

The shortest side is the one opposite the smallest angle. If the angle you already know is the shortest one, then the shortest side is opposite it. However, if the angle you already know is the medium one, then the shortest side is adjacent to it. The hypotenuse is always the longest side in a right triangle because it is opposite of the largest angle, the ninety degree angle. Trigonometry is very useful in any type of physics, engineering, meteorology, navigation, etc... (Wherever geometry is useful, trig is almost certain to also be useful). Trig isn't for everyone, however if little billy wants to calculate how tall a building is without producing the world's longest tape measure, he's gonna need some trig. The name sine (from what i know) comes from the latin word sinus, meaning hole or cavity, basically translation after translation of the word we ended with hole, which turned into sinus, sine for short (I may be wrong, but that is what I remember). The name cosine comes from the fact that sine and cosine are co-functions, (due to the fact that sin(x-90)=cosx. Tangent is not as easy to explain, it has to do with geometry and tangent lines. Trigonometry is part of the standard high school curriculum, but it's not an essential subject for nothing. Many career choices involve studying trigonometry, especially STEM fields such as science, engineering, or technology. In the end, it depends on you and your career choice. Because, if anything, trigonometry is very useful for...

Hypotenuse In Mathematics, the term “Hypotenuse” comes from the Greek word hypoteinousa that means “stretching under”. This term is used in Geometry, especially in the Table of Contents: • • • • • • • • Hypotenuse Meaning Hypotenuse means, the longest side of a right-angled triangle compared to the length of the base and perpendicular. The hypotenuse side is opposite to the right angle, which is the biggest angle of all the three angles in a right triangle. Basically, the hypotenuse is the property of only the right triangle and no other triangle. Now, this is better explained when we learn about the right-angled theorem or Hypotenuse Theorem The hypotenuse theorem is defined by Pythagoras theorem, According to this theorem, the square of the hypotenuse side of a right-angled triangle is equal to the sum of squares of base and perpendicular of the same triangle, such that; Hypotenuse 2 = Base 2 + Perpendicular 2 Hypotenuse Formula The formula to find the hypotenuse is given by the square root of the sum of squares of base and perpendicular of a right-angled triangle. The hypotenuse formula can be expressed as; Hypotenuse = √[Base 2 + Perpendicular 2] Let a, b and c be the sides of the triangle as per given figure below; So the hypotenuse formula for this triangle can be given as; c 2 = a 2 + b 2 Where a is the perpendicular, b is the base and c is the hypotenuse. Also, read: • • • • Hypotenuse Theorem Proof Given: A right triangle ABC, right-angled at B. To Prove: Hyp...

Hypotenuse In Mathematics, the term “Hypotenuse” comes from the Greek word hypoteinousa that means “stretching under”. This term is used in Geometry, especially in the Table of Contents: • • • • • • • • Hypotenuse Meaning Hypotenuse means, the longest side of a right-angled triangle compared to the length of the base and perpendicular. The hypotenuse side is opposite to the right angle, which is the biggest angle of all the three angles in a right triangle. Basically, the hypotenuse is the property of only the right triangle and no other triangle. Now, this is better explained when we learn about the right-angled theorem or Hypotenuse Theorem The hypotenuse theorem is defined by Pythagoras theorem, According to this theorem, the square of the hypotenuse side of a right-angled triangle is equal to the sum of squares of base and perpendicular of the same triangle, such that; Hypotenuse 2 = Base 2 + Perpendicular 2 Hypotenuse Formula The formula to find the hypotenuse is given by the square root of the sum of squares of base and perpendicular of a right-angled triangle. The hypotenuse formula can be expressed as; Hypotenuse = √[Base 2 + Perpendicular 2] Let a, b and c be the sides of the triangle as per given figure below; So the hypotenuse formula for this triangle can be given as; c 2 = a 2 + b 2 Where a is the perpendicular, b is the base and c is the hypotenuse. Also, read: • • • • Hypotenuse Theorem Proof Given: A right triangle ABC, right-angled at B. To Prove: Hyp...