Question

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. a=28, b=15, ∠A=110∘

Answer 1

To solve the given problem, we can use the Law of Sines to find the measure of angle B and the lengths of sides b and c. There are two possible triangles that satisfy the given conditions.

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. In this case, we have the values of sides a and b, and the measure of angle A. We can use the Law of Sines to calculate the measure of angle B and the lengths of sides b and c.

1. First, use the Law of Sines to find the measure of angle B: sin B = (b * sin A) / a. Substitute the given values: sin B = (15 * sin 110) / 28. Calculate sin B: sin B ≈ 0.7087.
2. Next, find the measure of angle B using the inverse sine function: B = sin^(-1)(0.7087). Calculate B: B ≈ 44.29°.
3. Now, use the Law of Sines to find the lengths of sides b and c: b / sin B = c / sin A. Substitute the given values and the calculated angles: 15 / sin 44.29 = c / sin 110. Solve for c: c ≈ 21.97.

Therefore, there are two possible triangles that satisfy the given conditions: one with angle B ≈ 44.29°, side b ≈ 15, and side c ≈ 21.97; and another with angle B ≈ 135.71° (180° - 44.29°), side b ≈ 15, and side c ≈ 21.97.