91Ó°ÊÓ

An airplane flies 165 miles from point \(A\) in the direction \(130^{\circ}\) and then travels in the direction \(245^{\circ}\) for 80 miles. Approximately how far is the airplane from \(A ?\)

A motorboat traveled along a triangular course having sides of lengths 2 kilometers, 4 kilometers, and 3 kilometers, respectively. The first side was traversed in the direction \(\mathrm{N} 20^{\circ} \mathrm{W}\) and the second in a direction \(\mathrm{S} \theta^{\circ} \mathrm{W}\). where \(\theta^{\circ}\) is the degree measure of an acute angle. Approximate, to the nearest minute, the direction in which the third side was traversed.

Surveying A surveyor notes that the direction from point \(A\) to point \(B\) is \(\ 63^{\circ} \mathrm{W}\) and the direction from \(A\) to point \(C\) is S38 \(^{\circ} \mathrm{W}\). The distance from \(A\) to \(B\) is 239 yards, and the distance from \(B\) to \(C\) is 374 yards. Approximate the distance from \(A\) to \(C\).

The magnitudes and directions of two forces acting at a point \(P\) are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. $$\text { (a) } 90 \text { Ib, } \mathrm{N} 75^{\circ} \mathrm{W} \quad \text { (b) } 60 \mathrm{lb}, \quad \mathrm{S} 5^{\circ} \mathrm{E}$$