Use the Law of Sines to find the missing angle of the triangle.
Find m∠B to the nearest tenth.
triangle
(1 point)
Responses
110.0º
110.0º
153.9º
153.9º
26.1º
26.1º
70.0º
To find the missing angle, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
To find angle B, we can use the following equation:
sin(B)/b = sin(A)/a
where angle A is 70 degrees, side a is 12 units, and side b is 20 units.
Plugging in the values we have:
sin(B)/20 = sin(70 degrees)/12
sin(B) = 20 * sin(70 degrees) / 12
sin(B) = 0.9397
Now, we can solve for angle B by taking the inverse sine of 0.9397:
B = sin^(-1)(0.9397)
B ≈ 69.0 degrees
Therefore, angle B is approximately 69.0 degrees.
The closest option provided is 70.0º.