10.1E: Non-right Triangles - Law of Sines (Exercises)

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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.

$Triangle with standard labels. Angle A is 36 degrees with opposite side a unknown. Angle B is 24 degrees with opposite side b = 16. Angle C and side c are unknown.$

4. Find the area of the triangle.

$A triangle. One angle is 75 degrees with opposite side unknown. The adjacent sides to the 75 degree angle are 8 and 11.$

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.

$Diagram of a plane flying over a highway. It is to the left and above points A and B on the ground in that order. There is a horizontal line going through the plan parallel to the ground. The angle formed by the horizontal line, the plane, and the line from the plane to point B is 25 degrees. The angle formed by the horizontal line, the plane, and point A is 49 degrees.$

Figure 1