A triangle ABC with side AB marked as c, side BC as a which is equal to 10 inches, and CA as b which is equal to 15 inches. Angle ACB is labeled 40 degrees and angle ABC is labeled 85 degrees.
Use the Law of Sines to find the value of side length c. Round to the nearest tenth of an inch.
(1 point)
Responses
9.7 inches
9.7 inches
6.5 inches
6.5 inches
0.2 inches
0.2 inches
15.5 inches
15.5 inches
To find the length of side c using the Law of Sines, you can use the following formula:
c / sin(C) = a / sin(A)
Where:
c is the side opposite angle C (10 inches),
C is angle ACB (40 degrees),
a is the side opposite angle A,
A is angle ABC (85 degrees).
Plugging in the values:
c / sin(40) = 15 / sin(85)
c / sin(40) = 15 / sin(85)
c / sin(40) = 15 / sin(85)
c = 15 * sin(40) / sin(85)
c ≈ 9.7 inches
Therefore, the value of side length c is approximately 9.7 inches.