There is a triangle inside of a circle. I have to find area of the shaded region which is the circle. So i would have to substract the area of the triangle from the area of the circle.

the radius of the circle is 3 inches.
I found the area of the circle..it is 28.27 in.^2

I am given the three angles of the triangle- 80 degrees, 55 degrees, and 45 degrees

how would I find the area of the triangle with the given 3 angles?? plz help with steps!

if 5/17 of a region is shaded, what part is not shaded?

To find the area of a triangle with the given angles, you can use the Law of Sines to find the ratio of the side lengths. Here are the steps:

1. Calculate the length of one side of the triangle.
- Assume any length for the side and label it as 'a'.

2. Use the Law of Sines to find the ratios of the sides.
- The Law of Sines states that the ratio of the lengths of the sides of a triangle is equal to the ratio of the sines of their opposite angles.

- Divide each angle by the sine of its respective angle:
- For angle A with side a: a / sin(A)
- For angle B with side b: b / sin(B)
- For angle C with side c: c / sin(C)

3. Find the ratio of the sides.
- Since you assumed side a with length 'x', you can now set up the proportion: x / sin(A) = a / sin(A).
- Solve the proportion for side a by multiplying both sides by sin(A):
- x = a * sin(A)

4. Calculate the lengths of the other two sides.
- Use the ratios to find the lengths of the other two sides.
- Multiply side a with sin(B) to get side b: b = a * sin(B).
- Multiply side a with sin(C) to get side c: c = a * sin(C).

5. Use Heron's Formula to calculate the area of the triangle.
- Heron's Formula states that the area of a triangle with side lengths a, b, and c is given by:
- Area = sqrt(s * (s - a) * (s - b) * (s - c))
- Where s is the semi-perimeter: s = (a + b + c) / 2.

6. Plug in the values and calculate the area of the triangle.
- Substitute the lengths of the sides into the formula and evaluate.

Now, you can subtract the area of the triangle from the area of the circle to find the shaded area.

To find the area of a triangle given the three angles, you can use the law of sines or the law of cosines. However, since you have the measures of all three angles, you can use a simpler method known as the sine formula. Here are the steps to find the area of the triangle:

1. Start by drawing the triangle and label the angles A, B, and C.
- Angle A is 80 degrees.
- Angle B is 55 degrees.
- Angle C is 45 degrees.

2. Next, draw the circumcircle of the triangle, which is the circle passing through all three vertices of the triangle.

3. To find the area of the triangle, we need to find the length of at least one side of the triangle. Since the triangle is inscribed in a circle, we can use the fact that the lengths of the sides of an inscribed triangle are related to the radius of the circle.

4. In this case, the radius of the circle is 3 inches.

5. We'll use the formula for the length of a side of a triangle inscribed in a circle:
Side length = 2 * Radius * sin(angle)

6. Calculate the side lengths using the formula for each side of the triangle:
- Side length a = 2 * 3 inches * sin(80 degrees)
- Side length b = 2 * 3 inches * sin(55 degrees)
- Side length c = 2 * 3 inches * sin(45 degrees)

7. Once you have the lengths of the sides of the triangle, you can use Heron's formula to find the area of the triangle.

8. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semiperimeter of the triangle calculated as s = (a + b + c) / 2.

9. Plug the lengths of the sides of the triangle into Heron's formula to get the area.

10. Once you have the area of the triangle, you can subtract it from the area of the circle to find the area of the shaded region.

In summary, to find the area of the triangle with given angles, use the sine formula to find the lengths of the sides, then apply Heron's formula to find the area.

12/17 duh!