10.1E: Non-right Triangles - Law of Sines (Exercises)
For the following exercises, assume \(\alpha\) is opposite side \(a, \beta\) is opposite side \(\mathbf{b},\) and \(\gamma\) is opposite side \(c .\) Solve each triangle, if possible. Round each answer to the nearest tenth.
1. \(\beta=50^{\circ}, a=105, \mathbf{b}=45\)
2. \(\alpha=43.1^{\circ}, a=184.2, \mathbf{b}=242.8\)
3. Solve the triangle.
4. Find the area of the triangle.
5. A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, \(2.1 \mathrm{~km}\) apart, to be \(25^{\circ}\) and \(49^{\circ}\), as shown in Figure 1 . Find the distance of the plane from point \(A\) and the elevation of the plane.
Figure 1