Exam 7: Applications of Trigonometry and Vectors

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 1 , - 3 \rangle , \mathbf { v } = \langle 4,2 \rangle$ . Find $- \mathbf { u } - \mathbf { v }$ .

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -A, c, and a

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. --12, 5

Solve the problem. -A ship leaves point A and travels directly north to point B. From point B, the ship then travels due east to point C. The magnitude of the vector from point A to point C is 140. Find the magnitude of The northern vector. Find the magnitude of the eastern vector.

Find the angle between the pair of vectors to the nearest tenth of a degree. - $\langle 4,5 \rangle , \langle - 4 , - 1 \rangle$

Solve the problem. -Two airplanes leave an airport at the same time, one going northwest (bearing 135°) at 414 mph and the other going east at 343 mph. How far apart are the planes after 4 hours (to the nearest Mile)?

Draw a sketch to represent the vector. Refer to the vectors pictured here. - $\mathbf { i } + 3 \mathbf { j } , 8 \mathbf { i } - \mathbf { j }$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - $\langle - 4 , - 3 \rangle$

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. -AB = 321 yd AC = 188 yd BC = 161 yd

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. -a = 26 ft b = 39 ft C = 40 ft

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 5 , - 5 \rangle , \mathbf { v } = \langle - 3,8 \rangle$ . Find $\mathbf { v } - \mathbf { u }$ .

Solve the problem. -An airplane is sighted at the same time by two ground observers who are 2 miles apart and both directly west of the airplane. They report the angles of elevation as 12° and 21°. How high is the Airplane? Round to the nearest hundredth of a mile.

Solve the problem. -A pilot wants to fly on a bearing of 62.5°. By flying due east, he finds that a 51-mph wind, blowing from the south, puts him on course. Find the ground speed of the plane.

Find the angle between the pair of vectors to the nearest tenth of a degree. -6i + 3j, -2i + 3j

Find the missing parts of the triangle. -A = 78° a = 36 yd B = 73 yd If necessary, round angles to the nearest degree and side lengths to the nearest yard.

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. --16, 0

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 9 , - 3 \rangle , \mathbf { v } = \langle - 1,8 \rangle$ . Find $- 6 \mathbf { u } + \mathbf { v }$ .

Find the angle between the pair of vectors to the nearest tenth of a degree. - $\langle - 9 , - 1 \rangle , \langle - 8,7 \rangle$

Solve the problem. -Suppose you would like to cross a 219-foot wide river in a boat. Assume that the boat can travel 38 mph relative to the water and that the current is flowing west at the rate of 7 mph. What bearing Should be chosen so that the boat will land at a point exactly across from its starting point? Give Your answer to the nearest tenth of a degree.