Answer :
Final answer:
To find the value of side a in triangle ABC, we first find angle B using the sum of angles in a triangle, then apply the tangent ratio for angle A to solve for a. The calculation gives an approximate value of 25.8 cm for side a, which does not match any of the provided options.
Explanation:
To solve for the value of a in the right triangle ABC with C = 90 degrees, A = 35.6 degrees, and b = 35.9 cm, we first determine the angle B. Since the sum of angles in any triangle is 180 degrees, we can find angle B by subtracting the known angles from 180 degrees:
B = 180 degrees - A - C
B = 180 degrees - 35.6 degrees - 90 degrees
B = 54.4 degrees
Now we'll use the tangent of angle A to find the length of side a, knowing the length of side b:
tan(A) = opposite/adjacent
tan(35.6 degrees) = a / 35.9 cm
Multiplying both sides by 35.9 cm to isolate a:
a = 35.9 cm * tan(35.6 degrees)
Calculating the value of tan(35.6 degrees) and multiplying by 35.9 cm yields the value of a:
a \u2248 35.9 cm * 0.7162
a \u2248 25.7 cm
Rounded to the nearest tenth, the value of a is 25.8 cm, which is not listed in the options provided.