Use the Law of Sines to find the value of side length c. Round to the nearest tenth of an inch.
15.5 inches
15.5 inches
9.7 inches
9.7 inches
0.2 inches
0.2 inches
6.5 inches
To use the Law of Sines, we can set up the following equation:
sin(A) / a = sin(B) / b = sin(C) / c
Given the side lengths:
a = 15.5 inches
b = 9.7 inches
c = ?
Let's assume angle A is opposite side a and angle B is opposite side b.
We also know that the sum of angles in a triangle is 180 degrees, so:
A + B + C = 180
We can rearrange this equation to solve for angle C:
C = 180 - A - B
Now, we can substitute the values into the Law of Sines equation:
sin(A) / a = sin(B) / b = sin(C) / c
sin(A) / 15.5 = sin(B) / 9.7 = sin(C) / c
We need to find the value of side c. Let's isolate it in the equation:
sin(C) / c = sin(A) / 15.5
Cross-multiply:
c * sin(A) = 15.5 * sin(C)
Now, divide both sides by sin(A) to solve for c:
c = (15.5 * sin(C)) / sin(A)
To find the value of side c, we need the measures of angles A and C. Since we don't have the measures of these angles, we cannot accurately determine the value of side c using the Law of Sines.