Given TriangleABC with a = 9, b = 15, and m<A= 28 degrees, find the number of distinct solutions.
I got two solutions. Not sure if I am correct though.
sinB/b = sinA/a
sinB = 9(sin28)/15 = 0.2817
B = 16° or 164°
To determine the number of distinct solutions in Triangle ABC, we need to apply the Law of Sines. The Law of Sines states that in any triangle, the ratio of a side length to the sine of its corresponding angle is constant.
In this case, we know the lengths of sides a = 9 and b = 15, as well as the measure of angle A = 28 degrees. We can use the Law of Sines to find the measure of angle B.
Using the Law of Sines, we can set up the following equation:
a / sin(A) = b / sin(B)
Substituting the given values:
9 / sin(28°) = 15 / sin(B)
To find the value of sin(B), we can rearrange the equation:
sin(B) = 15 * sin(28°) / 9
Using the inverse sine function (sin⁻¹) on a calculator, we can find the approximate value of angle B:
B ≈ sin⁻¹(15 * sin(28°) / 9)
Once we have the approximate value of angle B, we can use the Triangle Sum Theorem to find angle C:
C = 180° - A - B
Using this information, we can determine the number of distinct solutions by considering the possibilities for angle B.