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# How to find the length of the hypotenuse in a right-angled triangle

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The hypotenuse is called the longest side inRectangular triangle, so it's no surprise that the Greek translates this word as "stretched". This side always lies opposite the angle of 90 °, and the sides forming this angle are called cathets.

Knowing the lengths of these sides and the magnitude of acute angles in different combinations of these values, one can calculate the length of the hypotenuse.

Instructions

1

If the lengths of both legs of the triangle (AAnd B), then use to find the length of the hypotenuse (C), the most, perhaps, known on our planet mathematical postulate - the theorem of Pythagoras. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, from which it follows that you should calculate the square root of the sum of the squared lengths of the two known sides: C =? (A? + B?). For example, if the length of one leg is 15 centimeters and the other is 10 centimeters, the length of the hypotenuse will be approximately 18,0277564 centimeters, since? (15? +10?) =? (225 + 100) =? 325? 18.0277564 .

2

If the length of only one of the legs (A) is known,In a right-angled triangle, as well as the value of the angle opposite it (?), Then the length of the hypotenuse (C) can be determined using one of the trigonometric functions - the sine. To do this, divide the length of the known side by the sine of the known angle: C = A / sin (?). For example, if the length of one of the legs is 15 centimeters, and the angle in the opposite vertex of the triangle is 30 degrees, then the length of the hypotenuse will be 30 centimeters, since 15 / sin (30) = 15 / 0.5 = 30.

3

If in a rectangular triangle is knownThe value of one of the acute angles (?) And the length of the adjacent leg (B), then to calculate the length of the hypotenuse (C), you can use another trigonometric function - the cosine. You should divide the length of the known leg into the cosine of the known angle: C = B / cos (?). For example, if the length of this leg is 15 centimeters and the acute angle to it is 30 degrees, the length of the hypotenuse will be approximately 17.3205081 centimeters, since 15 / cos (30) = 15 / (0.5 * ? 3) = 30 /? 3? 17,3205081.

How to find the length of the hypotenuse in a right-angled triangle Was last modified: June 21st, 2017 By
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