How To Find Sides Of Right Triangle With Known Angles And Area?

In summary, the conversation is about finding the formula for calculating the screen size that will have the same area as another screen with a different aspect ratio. The formula involves using a right triangle with known angles and area, and the variables a, b, c, and A. The final formula is c = √(2A/cos θsin θ), a = √(2Acot θ), and b = √(2Atan θ).
  • #1
DaleSwanson
352
2
I'm comparing TV and monitor sizes, and I'm trying to figure out the formula that will let me find what size screen will have the same area as another screen (with different aspect ratios). This boils down to a right triangle with all the angles and the area known. Normally I'd find this on Google, but there are a large number of pages describing how to find the area with known sides or areas that are getting in the way.

So can someone post the formula for this?
 
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  • #2
Let a be the adjacent, let b be the opposite, and let c be the hypotenuse and A the area. Then

[tex]
\[
c = \sqrt{\frac{2A}{\cos \theta \sin \theta}}
\]
\[
a= \sqrt{2A \cot \theta}
\]
\[
b = \sqrt{2A \tan \theta}
\]
[/tex]
 
Last edited:
  • #3
Perfect, thanks.
 

1. How do I find the missing sides of a right triangle with known angles and area?

To find the missing sides of a right triangle, you can use the Pythagorean theorem or trigonometric ratios such as sine, cosine, and tangent. You will need to know at least one side and one angle of the triangle, as well as the area of the triangle.

2. Can I use the Pythagorean theorem to find the missing sides of any right triangle?

Yes, the Pythagorean theorem can be used to find the missing sides of any right triangle as long as you know the lengths of two sides. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

3. What are the trigonometric ratios used to find the missing sides of a right triangle?

The three main trigonometric ratios used to find the missing sides of a right triangle are sine, cosine, and tangent. Sine is the ratio of the opposite side to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

4. How many pieces of information do I need to know to find the missing sides of a right triangle?

You will need to know at least one side and one angle of the right triangle, as well as the area of the triangle. With this information, you can use the Pythagorean theorem or trigonometric ratios to find the missing sides.

5. Is there a formula for finding the missing sides of a right triangle with known angles and area?

Yes, there is a formula known as the area formula that can be used to find the missing sides of a right triangle with known angles and area. This formula is A = (1/2)bh, where A is the area of the triangle, b is the base, and h is the height. This formula is useful when you know the area and one side of the triangle, as it allows you to solve for the missing side.

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