Question

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. a=20, c=45, A=∠A=125°

Answer 1

To use the Law of Sines, set up proportions using given values and solve for unknown angles and sides.

Step-by-step explanation:

To solve for all possible triangles that satisfy the given conditions, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. Using the given information, we have:

1. a = 20
2. c = 45
3. A = ∠A = 125°

Let's label the remaining side b and the remaining angles B and C.

Using the Law of Sines, we can set up the following proportions:

a/sinA = b/sinB = c/sinC

Substituting the given values, we have:

20/sin125° = b/sinB = 45/sinC

Solving for sinB and sinC, we can find the possible values for angle B and angle C, which will give us the corresponding values for side b:

sinB = (20/sin125°) * sinB

sinC = (45/sin125°) * sinC