# Solving Right Triangles with 3 Angles and Area - Warren

• Whalstib
In summary, the conversation was about solving a right triangle given 3 angles and the area. They discussed using the Law of Sines and the formula for area using two sides and their internal angle to determine a constant. The conversation concluded with the suggestion to use the formula A_{triangle} = \frac{1}{2}ab \sin(\gamma) to solve the triangle.
Whalstib
But I'm not getting it.

Is it possible to solve a right triangle give 3 angles and the area?

For instance 90-72-18, A=150.

What I'm trying to solve is a problem of squares to rectangles and vis versa using trigonometry. I'll use this to determine extension and contraction.

Thanks,

Warren

Law of Sines will give you the relation between the sides, hence the sides up to a constant. Use the formula for area using two sides and their internal angle to determine this constant.

I was going in that direction but have only used this to solve SAS etc problems.

So far I have a/.31=b/.95=c/1

Could you elaborate please..

thanks,

Warren

Oh I got it!

Thanks!

Warren

Using $$A_{triangle} = \frac{1}{2}ab \sin(\gamma)$$, where a and b are sides of the triangle, and gamma is the angle between them should give you enough information to solve the triangle.

Edit: too late...

## 1. What is the formula for finding the area of a right triangle?

The formula for finding the area of a right triangle is A = 1/2 * base * height. This means that you will take half of the length of the base of the triangle and multiply it by the height of the triangle.

## 2. How many angles are needed to solve a right triangle?

To solve a right triangle, you need to know the measures of at least two angles. This can include the three angles of the triangle or one angle and the right angle, since the sum of the angles in a triangle is always 180 degrees.

## 3. Can you use trigonometric functions to solve a right triangle with 3 angles and area?

Yes, you can use trigonometric functions such as sine, cosine, and tangent to solve a right triangle with 3 angles and area. These functions can help you find the missing side lengths of the triangle, which in turn can be used to calculate the area.

## 4. What is the Pythagorean theorem and how does it apply to solving right triangles?

The Pythagorean theorem states that in a right triangle, 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. This theorem is often used to find the length of a missing side in a right triangle.

## 5. What are some real-world applications of solving right triangles with 3 angles and area?

Real-world applications of solving right triangles with 3 angles and area include architecture, engineering, and navigation. For example, architects use right triangles to determine the dimensions of buildings and engineers use them to design structures and machines. In navigation, right triangles can be used to calculate distances and angles to help navigate a course.

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