Right Isosceles triangle: solve for the length of the unknown legs

MHB
Thread starter urekmazino
Start date Jan 31, 2019
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Length Triangle

In summary, a right isosceles triangle is a triangle with a right angle and two equal sides. The Pythagorean theorem can be used to solve for the length of the unknown legs in a right isosceles triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides. The length of any side in a triangle cannot be negative, and there is a specific formula (c = a√2) for finding the length of the unknown legs in a right isosceles triangle. The Pythagorean theorem can also be used to solve for the length of the unknown legs in any right triangle, not just a right isosceles triangle, as long as

Jan 31, 2019

urekmazino

For a right isosceles triangle (45-45-90) of hypotenuse 1, solve for the length of the unknown legs. Give an exact answer and rationalize the denominator in the final answer.

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Jan 31, 2019

kaliprasad

Gold Member

MHB

kindly in form what you have tried so that we can help you

Jan 31, 2019

HOI

Call the length of each leg "x" and set up the Pythagorean theorem. Solve for x.

1. What is a right isosceles triangle?

A right isosceles triangle is a triangle with two equal sides and one right angle. This means that the two legs of the triangle are equal in length and the third side, called the hypotenuse, forms a right angle with one of the legs.

2. How do you solve for the length of the unknown legs in a right isosceles triangle?

To solve for the length of the unknown legs in a right isosceles triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, since the two legs are equal, you can set up the equation as x^2 + x^2 = c^2, where x represents the length of the unknown legs and c represents the length of the hypotenuse. Solving for x will give you the length of the unknown legs.

3. Can you use trigonometry to solve for the length of the unknown legs in a right isosceles triangle?

Yes, you can also use trigonometry to solve for the length of the unknown legs in a right isosceles triangle. Since the triangle has a right angle, you can use the trigonometric ratios of sine, cosine, and tangent to find the length of the unknown legs. For example, if you know the length of the hypotenuse and one of the acute angles, you can use the sine ratio (sinθ = opposite/hypotenuse) to find the length of the unknown leg.

4. Are there any special properties of a right isosceles triangle?

Yes, there are a few special properties of a right isosceles triangle. As mentioned before, it has two equal sides and one right angle. Additionally, the altitude drawn from the right angle to the hypotenuse will bisect the hypotenuse, meaning it will divide it into two equal parts. Also, the two acute angles in a right isosceles triangle are always 45 degrees each.

5. Can a right isosceles triangle be used in real-life applications?

Yes, right isosceles triangles have many real-life applications. For example, they are commonly used in construction to create stable and sturdy structures. The 45-degree angles make them ideal for supporting weight and distributing forces evenly. They are also used in navigation and surveying, as well as in various engineering and design fields.