Use the given information to solve the triangle.

1) C = 145 degrees, b = 4, c = 14.

2) A = 150 degrees, C = 20 degrees, a = 200.

sinB = b sinC/c

having B you now have A = 180 - (B+C)

a = c sinA/sinC

the second is easier. You already know that B = 10 degrees. now just use b/sinB = c/sinC = a/sinA

To solve both triangles, we can use the Law of Sines or the Law of Cosines, depending on the information we are given. Let's use the information from each triangle to solve them one by one.

Triangle 1:
Given: C = 145 degrees, b = 4, c = 14.
We are given the angle C and the measures of two sides, b and c. To solve this triangle, we can use the Law of Sines or the Law of Cosines.

Using the Law of Sines:
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. So we have:
sin(A)/a = sin(B)/b = sin(C)/c

In this case, we are trying to find the angle A. Since we know angle C and the sides b and c, we can set up the equation as follows:
sin(145 degrees)/4 = sin(A)/14

Now we can solve for the unknown angle A using trigonometric functions and find the third angle B (since the sum of angles in a triangle is 180 degrees). Once we have all three angles, we can use the Law of Sines again to find the remaining side lengths.

Triangle 2:
Given: A = 150 degrees, C = 20 degrees, a = 200.
In this triangle, we are given the angle A, the angle C, and the side a. Again, we can use either the Law of Sines or the Law of Cosines to solve this triangle.

Using the Law of Sines:
Set up the equation using the Law of Sines:
sin(A)/a = sin(B)/b = sin(C)/c

In this case, we are trying to find the unknown side length b. Since we know the angles A and C and the side a, we can set up the equation as follows:
sin(150 degrees)/200 = sin(B)/b

Solve for the remaining side length b using trigonometric functions. After finding side b, we can use the Law of Sines again to find the remaining side length c.