Given ABC with a = 9, b = 5, and mA 80° , find mB . Round the sine value to the nearest thousandth and answer to the nearest whole degree.
I got 33° am I right?
sinB/b = sinA/A
sinB/5 = sin80°/9
sinB = 0.5471
B = 33.17°
good work
Use Law of Sines:
SinA/a = SinB/b.
Sin80/9 = SinB/5,
SlnB = 5/9 * Sin80 = 0.5471.
B = 33.o.
To find the measure of angle B in triangle ABC, you can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides and angles.
First, you need to find the length of side c. Since you know the lengths of sides a and b, you can use the Law of Cosines, which states that c² = a² + b² - 2ab * cos(C), to find side c. In this case, angle C is opposite side c.
Using the Law of Cosines, you can calculate c:
c² = 9² + 5² - 2 * 9 * 5 * cos(80°)
c² = 81 + 25 - 90 * cos(80°)
c² = 106 - 90 * cos(80°)
c² ≈ 106 - 90 * (-0.173648)
c² ≈ 106 + 15.62112
c² ≈ 121.62112
c ≈ √121.62112
c ≈ 11.033627
Now that you have the length of side c, you can use the Law of Sines to find the measure of angle B.
sin(B) / b = sin(A) / a
sin(B) / 5 = sin(80°) / 9
To solve for sin(B), you can cross-multiply:
sin(B) = 5 * sin(80°) / 9
Now, calculate sin(B):
sin(B) ≈ 5 * 0.984808 / 9
sin(B) ≈ 0.546015
To find the measure of angle B, you can use the arcsine function (sin⁻¹) or a calculator that has an inverse sine function. Round the sine value to the nearest thousandth before calculating the arcsine:
B ≈ sin⁻¹(0.546)
Using a calculator, you would find that B ≈ 33.025 degrees.
Therefore, the measure of angle B is approximately 33 degrees (rounded to the nearest whole degree). Your answer is correct!