91Ó°ÊÓ

________ Theorem states that if \(z = r(\cos\ \theta + i \sin\ \theta)\) is a complex number and \(n\) is a positive integer, then \(z^{n} = r^{n}(\cos\ n\theta + i \sin\ n\theta)\).

The set of all directed line segments that are equivalent to a given directed line segment \(\overset{\rightharpoonup} {\small PQ}\) is a ________ \(\small{\mathbf{v}}\) in the plane.

The Law of Cosines can be used to establish a formula for finding the area of a triangle called ________ ________ Formula.

The directed line segment whose initial point is the origin is said to be in ________ ________ .

In Exercises 5-24, use the Law of Sines to solve the triangle.Round your answers to two decimal places. \(A\ =\ 102.4^{\circ}\), \(C\ =\ 16.7^{\circ}\), \(a\ =\ 21.6\)

In Exercises 5-20, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. \(a = 55\), \(b = 25\), \(c = 72\)

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((-3, 11)\) Terminal Point - \((9, 40)\)

NAVIGATION A boat race runs along a triangular course marked by buoys \(A\), \(B\), and \(C\). The race starts with the boats headed west for 3700 meters. The other two sides of the course lie to the north of the first side, and their lengths are 1700 meters and 3000 meters. Draw a figure that gives a visual representation of the situation, and find the bearings for the last two legs of the race.

NAVIGATION A plane flies 810 miles from Franklinto Centerville with a bearing of \(75^{\circ}\). Then it flies 648 miles from Centerville to Rosemount with a bearing of \(32^{\circ}\). Draw a figure that visually represents the situation, and find the straight-line distance and bearing from Franklin to Rosemount.

SURVEYING A triangular parcel of land has 115 meters of frontage, and the other boundaries have lengths of 76 meters and 92 meters. What angles does the frontage make with the two other boundaries?