hypotenuse definition math
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Pythagorean theorem Math Open Reference. Definition: The longest side of a right triangle. The side opposite the right angle. In a right triangle (one where one interior angle is 90°), the longest side is called the hypotenuse. It is always the side opposite the 90° angle. See Right Triangle definition.
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Why is it that the hypotenuse is the longest side of a right triangle? By definition, the hypotenuse is the side opposite of the right angle in the triangle. Because a triangle is only made of of 180deg, and the right angle is 90deg...no other angle can be larger than the right angle, hence no side can be longer than the side opposite the largest angle.
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- 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.
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Hypotenuse The length of the hypotenuse is calculated using the square root function implied by the Pythagorean theorem. Using the common notation that the length of the two legs of the triangle (the sides perpendicular to each other) are a and b and that of the hypotenuse is c, we have.or example, if one of the other sides has a length of 3 (when squared, 9) and the other has a length of 4 (when squared, 16), then their squares add up to 25. The length of the hypotenuse is the square root of 25, that is, 5.
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Right Triangles A Right Triangle's Hypotenuse. The hypotenuse is the largest side in a right triangle and is always opposite the right angle. (Only right triangles have a hypotenuse). The other two sides of the triangle, AC and CB are referred to as the 'legs'. In the triangle on the left, the hypotenuse is the side AB which is opposite the right angle, $$ \angle C $$.
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- For any right triangle with non-hypotenuse sides of length 3 and 4 units, the hypotenuse will be 5 units in length. Because units are arbitrary, this relationship extends to multiple of 3, 4, and 5. 9 and 12 are 3 times 3 and 4. So the hypotenuse is 3 times 5, or 15.
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- The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between <i>0</i> and <i>1</i> it defines the sine of the angle.
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Pythagorean Theorem The answer to the original problem is: The hypotenuse is 2 5 centimeters long or The hypotenuse is about 4.5 centimeters long. How to Simplify Inside a Radical. If a number in radical form is not a perfect square, you may be able to simplify that number by factoring.
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How to Use the Pythagorean Theorem The Pythagorean Theorem describes the lengths of the sides of a right triangle in a way that is so elegant and practical that the theorem is still widely used today. The theorem states that for any right triangle, the sum of the squares of the non-hypotenuse sides is equal to the square of the hypotenuse.
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Trigonometric functions Confidence votes 40.5K. The longest side of a right-angled triangle is always opposite the right-angle and is called the hypotenuse. 29 people found this useful.
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- Find the length of the hypotenuse. Using the Pythagorean theorem, a2 + b2 = c2, and replacing both a and b with the given measure, solve for c. The hypotenuse is. feet long. Use the ratio for cosine, adjacent over hypotenuse, to find the answer.
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Definition The Pythagorean identities in trigonometry are the three identities that come from the Pythagorean theorem. Recall that the Pythagorean theorem states that the hypotenuse squared of a right triangle is the sum of the square of each of the other two sides. The Pythagorean theorem.
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trigonometric function sine, sin - ratio of the length of the side opposite the given angle to the length of the hypotenuse of a right-angled triangle. arc sine, arcsin, arcsine, inverse sine - the inverse function of the sine; the angle that has a sine equal to a given number.
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- Find the length of the hypotenuse of a right triangle whose legs are 3 and square root of 2. 2 square root of 2 square root of 11 square root of 13.
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- The name hypotenuse is given to the longest edge in a right-angled triangle. (It is the edge opposite to the right angle and is c in this case.) Where (for brevity) it says 'edge a', 'angle B' and so on, it should, more correctly, be something like 'length of edge a' or 'edge-length' or 'size of angle B' etc.
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Hypotenuse In geometry, a hypotenuse (alternate spelling: hypothenuse) is the longest side of a right-angled triangle, the side opposite of the right angle.
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Trigonometry The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A.
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- 10' is the length of the hypotenuse. Hypotenuse length practice: Find the length of the hypotenuse using the two sides given. Convert the numbers with units of measurement to include fractions. Round off the rest of the numbers to 4 decimal places.
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hypotenuse Origin of hypotenuse. Classical Latin hypotenusa ; from Classical Greek hypoteinousa, literally , subtending, properly feminine of present participle of hypoteinein, to subtend, stretch under ; from hypo-, under (see hypo-) + teinein, to stretch: see hypo- and amp; thin. also hy·poth·e·nuse.
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How to Find the Length of the Hypotenuse All right triangles have one right (90-degree) angle, and the hypotenuse is the side that is opposite or the right angle, or the longest side of the right triangle. The hypotenuse is the longest side of the triangle, and it’s also very easy to find using a couple of different methods. This article will teach you how to find the length of the hypotenuse using the Pythagorean theorem when you know the length of the other two sides of the triangle.
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How to Find the Length of the Hypotenuse How to Find the Length of the Hypotenuse. Three Methods: Using the Pythagorean Theorem Finding the Hypotenuse of Special Right Triangles Finding the Hypotenuse Using the Law of Sines. All right triangles have one right (90-degree) angle, and the hypotenuse is the side that is opposite that angle.
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Right Triangle Congruence Hypotenuse-Acute (HA) Angle Theorem. If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.
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45-45-90 Right Triangles Answer: The length of the hypotenuse is \(3\sqrt 2 \) inches. You can also recognize a 45°-45°-90° triangle by the angles. As long as you know that one of the angles in the right-angle triangle is 45°-45°-90° special right triangle.
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- The hypotenuse is the side of a right triangle that is directly across from the right angle (indicated by the black square in the picture at the left). The shorter sides of a right triangle are called the legs of the triangle (sides AB and BC in the picture at the right). Together the legs form the right angle of the right triangle. The medians of a triangle are line segments formed by connecting a vertex to the midpoint of the opposite side.
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Use the Pythagorean Theorem for Right Triangles... The theorem states that the hypotenuse of a right triangle can be easily calculated from the lengths of the sides. The hypotenuse is the longest side of a right triangle. If you're given the lengths of the two sides it is easy to find the hypotenuse.nswer : Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is [tex]a^2+b^2=c^2[/tex], which is known as the Pythagorean Theorem.
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- In the following right triangle PQR, 1  the side PQ, which is opposite to the right angle PRQ is called the hypotenuse. ( 2 The hypotenuse is the longest side of the right triangle.).3  the side RQ is called the adjacent side of angle θ. 4  the side PR is called the opposite side of angle θ.) for angle x b) for angle y. Solution: a) For angle x: AB is the hypotenuse, AC is the adjacent side, and BC is the opposite side. b) For angle y: AB is the hypotenuse, BC is the adjacent side, and AC is the opposite side.