Use the given information to solve the triangle. If two solutions exists, find both.

A=110 degrees
a=125
b=100

a is greater than b so I think that there is only one triangle. I am not sure where to go from here.

To solve the triangle given the information provided (A = 110 degrees, a = 125, b = 100), we can use the Law of Sines and the Law of Cosines. However, based on the given information, there seems to be an ambiguity in the triangle, as there could potentially be two solutions.

Here's how we can approach this problem step by step:

1. Start by drawing a triangle and labeling the given information. Label angle A as 110 degrees, side a as 125 units, and side b as 100 units.

2. Since we have an angle-side-side () scenario, we will first calculate angle B using the Law of Sines. The Law of Sines states that for any triangle:
sin(A) / a = sin(B) / b

Substitute the given values:
sin(110) / 125 = sin(B) / 100

Cross-multiply to solve for sin(B):
sin(B) = (sin(110) * 100) / 125

Use inverse sine (sin^(-1)) to find the value of B:
B = sin^(-1)[(sin(110) * 100) / 125]

Evaluate the value of B using a calculator.

3. Use the Law of Sines again to find angle C. The sum of the angles in a triangle is 180 degrees, so:
C = 180 - A - B

4. Now that we have all three angles, we can use the Law of Sines to find the remaining side length, c. The Law of Sines states:
a / sin(A) = c / sin(C)

Substitute the values:
125 / sin(110) = c / sin(C)

Cross-multiply and solve for c:
c = (125 * sin(C)) / sin(110)

Evaluate the value of c using a calculator.

5. Check for the ambiguity condition. Since a is greater than b, if the value of c obtained in step 4 is less than b, then there are two possible triangles that satisfy the given conditions. Otherwise, there is only one solution.

Following these steps, you should be able to determine both possible solutions if they exist or find the solution for the triangle.