![]() This forms two right triangles, although we only need the right triangle that includes the first tower for this problem. To answer the questions about the phone’s position north and east of the tower, and the distance to the highway, drop a perpendicular from the position of the cell phone, as in (Figure). Generally, triangles exist anywhere in the plane, but for this explanation we will place the triangle as noted. In geometry, an isosceles triangle is a triangle that has two sides of equal length. Complete step-by-step solution: We need to find the hypotenuse of an isosceles right triangle. Here is how it works: An arbitrary non-right triangle\,ABC\,is placed in the coordinate plane with vertex\,A\,at the origin, side\,c\,drawn along the x-axis, and vertex\,C\,located at some point\,\left(x,y\right)\,in the plane, as illustrated in (Figure). We need to apply Pythagoras theorem on this triangle, so we can find out the required solution. The derivation begins with the Generalized Pythagorean Theorem, which is an extension of the Pythagorean Theorem to non-right triangles. Understanding how the Law of Cosines is derived will be helpful in using the formulas. However, once the pattern is understood, the Law of Cosines is easier to work with than most formulas at this mathematical level. At first glance, the formulas may appear complicated because they include many variables. Three formulas make up the Law of Cosines. The tool we need to solve the problem of the boat’s distance from the port is the Law of Cosines, which defines the relationship among angle measurements and side lengths in oblique triangles. ![]() Using the Law of Cosines to Solve Oblique Triangles
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