Final answer:
To find the length of side c given angle b (130°), angle c (30°), and the length of side b (17 inches), apply the Law of Sines. Calculate c by using the formula c = b × (sin(C) / sin(B)) and substitute the known values.
Step-by-step explanation:
The student's question involves finding the length of side c in a triangle, given the measurement of angle b (130°), angle c (30°), and the length of side b (17 inches). This is an application of the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.
According to the Law of Sines,
a/sin(A) = b/sin(B) = c/sin(C). We are looking to find c, and we already know b and angles B and C. By using the formula:
c = b × (sin(C) / sin(B)), we can calculate the length of side c.
Substituting the given values into the formula:
c = 17 inches × (sin(30°) / sin(130°))
c = 17 inches × (0.5 / sin(130°))
Calculating the sine of 130° and performing the multiplication will give us the required length for side c, which is to be rounded to the nearest whole number.