Answer :
Final answer:
To solve the question, angle B in degrees is calculated using the sum of angles in a triangle, resulting in 54.4 degrees, not cm. The question seems to have a misunderstanding between measuring an angle and finding the length of a side. The provided options do not directly answer the posed question.
Explanation:
To find the length of side B in a right triangle ABC, where C is 90 degrees, A is 35.6 degrees, and side b is 35.9 cm, we can use trigonometric ratios. Given angle A and side b, we can solve for side a (opposite to angle A) using the tangent function, since tangent of angle A = opposite / adjacent, but we're interested in finding side c (hypotenuse).
First, find angle B using the fact that the sum of angles in a triangle equals 180 degrees. So, B = 180 - 90 - 35.6 = 54.4 degrees. However, to find the length of side B (assuming a typo in the question and that we're looking for side c), we can use the sine of angle A = opposite/hypotenuse (b/c). Sin(35.6) = 35.9/c. Solving this gives us the length of side c.
However, the question's options seem to misunderstand the task. There seems to be confusion between finding the length of a side versus the measure of angle B. If purely finding B in cm, none of the options are correct as they don't align with the required calculation process or the question's intended outcome. For clarity, angle B was found to be 54.4 degrees, but finding its length in cm would require additional steps not outlined in the available choices.
