Question

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. a = 30, c = 40, ∠A = 37°

Answer 1

To solve for all possible triangles that satisfy the given conditions, use the Law of Sines. Set up the ratio a/sin(A) = c/sin(C) and substitute the given values. Solve for sin(C) and take the arcsine to find the measure of angle C.

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 for all sides and angles in a triangle. Here's how to apply it:

1. Start by setting up the ratio: a/sin(A) = c/sin(C), where a is the length of side a, A is the measure of angle A, c is the length of side c, and C is the measure of angle C.
2. Substitute the given values into the equation: 30/sin(37°) = 40/sin(C).
3. Now, solve for sin(C) by cross multiplying: sin(C) = (40 * sin(37°)) / 30.
4. Take the arcsine of both sides to find the measure of angle C: C = arcsin((40 * sin(37°)) / 30).

By solving for the measure of angle C, you can determine all possible triangles that satisfy the given conditions.