91Ó°ÊÓ

For each point given in polar coordinates, state the quadrant in which the point lies if it is graphed in a rectangular coordinate system. (a) \(\left(5,135^{\circ}\right)\) (b) \(\left(2,60^{\circ}\right)\) (c) \(\left(6,-30^{\circ}\right)\) (d) \(\left(4.6,213^{\circ}\right)\)

Angle between Forces Two forces of 128 lb and 253 lb act at a point. The resultant force is 320 lb. Find the angle between the forces.

Magnitudes of Forces A force of 176 lb makes an angle of \(78^{\circ} 50^{\prime}\) with a second force. The resultant of the two forces makes an angle of \(41^{\circ} 10^{\prime}\) with the first force. Find the magnitudes of the second force and of the resultant.

Assume a triangle ABC has standard labeling. (a) Determine whether SAA, ASA, SSA, SAS, or SSS is given. (b) Decide whether the law of sines or the law of cosines should be used to begin solving the triangle. \(a, c,\) and \(A\)

For each pair of polar coordinates, ( \(a\) ) plot the point, ( \(b\) ) give two other pairs of polar coordinates for the point, and ( \(c\) ) give the rectangular coordinates for the point. $$\left(5,-60^{\circ}\right)$$

Distance of a Ship from Its Starting Point Starting at point \(X,\) a ship sails \(15.5 \mathrm{km}\) on a bearing of \(200^{\circ},\) then turns and sails \(2.4 \mathrm{km}\) on a bearing of \(320^{\circ} .\) Find the distance of the ship from point \(X .\)

Bearing and Ground Speed of a Plane An airline route from San Francisco to Honolulu is on a bearing of \(233.0^{\circ} .\) A jet flying at 450 mph on that bearing encounters a wind blowing at 39.0 mph from a direction of \(114.0^{\circ} .\) Find the resulting bearing and ground speed of the plane.

Solve triangle. \(A=67.3^{\circ}, b=37.9 \mathrm{km}, c=40.8 \mathrm{km}\)

Which one of the following sets of data determines a unique triangle? A. \(A=50^{\circ}, B=50^{\circ}, C=80^{\circ}\) B. \(a=3, b=5, c=20\) C. \(A=40^{\circ}, B=20^{\circ}, C=30^{\circ}\) D. \(a=7, b=24, c=25\)

Given vectors u and v, find: (a) 2u (b) 2u+3v (c) \(\mathbf{v - 3 u .}\) $$\mathbf{u}=\langle- 1,2\rangle, \mathbf{v}=\langle 3,0\rangle$$