113k views
5 votes
Given triangle ABC with C = 90°, b = 50, and A = 36° 20′, find a.

A. 36.77
B. 29.62
C. 240.45
D. 40.28

1 Answer

6 votes

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.

User Prule
by
7.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories