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A 45-45-90 triangle is an isosceles right angled triangle.

If its two short sides are of length x units then, by Pythagoras, the hypotenuse is given by:

hypotenuse2 = x2 + x2 = 2x2

Taking square roots,

hypotenuse = sqrt(2x2) = sqrt(2)*x

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Q: Why do you need sqrt 2 to divide the hypotenuse of a 45-45-90 triangle?
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How do you find a missing length in isosceles triangle?

1) The hypotenuse side will ALWAYS be the the side w/ the radical 2. 2) So if you want to find the HYPOTENUSE of an ISOSCELES triangle, you MULTIPLY one of the LEGS by the the square root of 2. 3) If you want to find the LEG of an ISOSCELES triangle, you DIVIDE the HYPOTENUSE by the square root of 2. ***** Hypotenuse of an isosceles triangle= one leg divided by square root of 2. ***** Leg of an isosceles triangle= hypotenuse divided by the square root of 2. You can also get all the help you need through my page on Facebook, 'Your Help' Merna Awad-ElSols


How do you find the other 2 sides of the triangle if you know the hypotenuse?

You need more information unless it's a right triangle and a common pathagorean triangle, such as a 90 degree angle with a hypotenuse of 5 would have legs of 3 and 4.


What is a hypotenuse theorem?

If the hypotenuse of a right triangle is congruent to the corresponding part of another right triangle, then the triangles are congruent. ========================================== Another contributor, in shock, stopped by to point out: That may (or may not) be a "hypotenuse theorem", but you really need to be careful trying to use it, because it's not true!


Does the hypotenuse of a triangle represent a third dimension?

No, the hypotenuse of a triangle does not represent a third dimension. A triangle is a 2 dimensional figure consisting of only dimensions in terms of x and y. In order to be a 3d figure it would need dimensions defined in terms of x, y, and z.


How do you find an angle of a right triangle when 3 sides are given?

you need a calculator to do Sin-1 Opposite/hypotenuse OR Cos-1 Adjacent/Hypotenuse OR Tan-1 Opposite/Adjacent

Related questions

How do you find a missing length in isosceles triangle?

1) The hypotenuse side will ALWAYS be the the side w/ the radical 2. 2) So if you want to find the HYPOTENUSE of an ISOSCELES triangle, you MULTIPLY one of the LEGS by the the square root of 2. 3) If you want to find the LEG of an ISOSCELES triangle, you DIVIDE the HYPOTENUSE by the square root of 2. ***** Hypotenuse of an isosceles triangle= one leg divided by square root of 2. ***** Leg of an isosceles triangle= hypotenuse divided by the square root of 2. You can also get all the help you need through my page on Facebook, 'Your Help' Merna Awad-ElSols


What is the length of a hypotenuse?

A hypotenuse is the longest side of a right angled triangle. The length of a hypotenuse can be found using the Pythagorean Theorem. This states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This means that to find the length of the hypotenuse, you need to know the lengths of the other two sides.


How do you find the other 2 sides of the triangle if you know the hypotenuse?

You need more information unless it's a right triangle and a common pathagorean triangle, such as a 90 degree angle with a hypotenuse of 5 would have legs of 3 and 4.


How do you find the angle opposite of the hypotenuse of a triangle with all three sides known?

The only triangle that has a hypotenuse is a right-triangle. The hypotenuse is the side opposite the right angle, so the angle is always 90 degrees. In this case, if you're just finding the angle then you don't need to know what the side lengths are.


What is a hypotenuse theorem?

If the hypotenuse of a right triangle is congruent to the corresponding part of another right triangle, then the triangles are congruent. ========================================== Another contributor, in shock, stopped by to point out: That may (or may not) be a "hypotenuse theorem", but you really need to be careful trying to use it, because it's not true!


Does the hypotenuse of a triangle represent a third dimension?

No, the hypotenuse of a triangle does not represent a third dimension. A triangle is a 2 dimensional figure consisting of only dimensions in terms of x and y. In order to be a 3d figure it would need dimensions defined in terms of x, y, and z.


How do you find the hypotenuse when only one length is given?

If the only information you have is the length of one side of a triangle, there are an infinite number of triangles having that length. Since the hypotenuse is defined to be "The side opposite the right angle in a plane right triangle", you will need the length of the other side to find the hypotenuse using the Pythagorean theorem. Alternatively you need to know the other angles. Then you can use the appropriate trig function to find the length of the hypotenuse.


How do you find the length of the sides of a right triangle given the hypotenuse?

You can't. You need some more information. If you only know the length of the hypotenuse, you can draw an infinite number of different right triangles that all have the same hypotenuse.


How do you find an angle of a right triangle when 3 sides are given?

you need a calculator to do Sin-1 Opposite/hypotenuse OR Cos-1 Adjacent/Hypotenuse OR Tan-1 Opposite/Adjacent


The length of the hypotenuse of a triangle is 20 what is the shorter leg?

You need to know something else to solve: either the long leg or the angle edit: if it is a right triangle you can use a theorem to figure out the other sides. the smallest side is a, the hypotenuse is 2a, the longer leg is a * sqrt (3) if the hypotenuse is 20, the smaller leg is 10.


How do you find the height of a triangle if you only have the hypotenuse?

You can't. The hypotenuse alone isn't enough to tell you anything about the triangle. There are an infinite number of different right triangles that all have the same hypotenuse. In order to find anything else, you also need to know either the length of one leg, or else the size of one acute angle.


Why do we need to divide the area of a triangle by 2?

Because in effect a triangle is half of a 4 sided quadrilateral