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Solve the right triangle ABC, with angle C = 90 degrees. Given angle A = 35.6 degrees and side b = 35.9 cm, find the value of side B in cm.

A) 35.9
B) 54.8
C) 90.5
D) 120.2

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.

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