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

1 answer

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.
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