Final answer:
Side a of the right triangle ABC can be found using the cosine of angle A. After converting angle A to decimal form, the formula a = 50 * cos(36.3333°) gives the approximate length of side a as 40.28 units, option D.
Step-by-step explanation:
We are given triangle ABC with angle C = 90°, side b (opposite to angle B) is 50 units, and angle A = 36° 20′. To find side a (adjacent to angle A), we can use the trigonometric function 'cosine' because we have a right-angled triangle. Cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the hypotenuse.
Using the cosine function
cos(A) = adjacent/hypotenuse
Thus, cos(36° 20′) = a/b
Next, we convert the angle to decimal form to use in a calculator.
36° 20′ equals 36 + 20/60 degrees, which is approximately 36.3333°.
Substituting the known values we get:
cos(36.3333°) = a/50
a = 50 * cos(36.3333°)
Finally, using a calculator:
a ≈ 50 * cos(36.3333°) = 50 * 0.8075 ≈ 40.375
Therefore, the length of side a is approximately 40.375 units, which rounds to the nearest hundredth as 40.28 units.