Exam 7: Applications of Trigonometry and Vectors

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

Sketch the vectors u and w with angle between them and sketch the resultant. -c - d

Solve the problem. -Suppose you would like to cross a 205-foot wide river in a boat. Assume that the boat can travel 33 mph relative to the water and that the current is flowing west at the rate of 5 mph. If the bearing is Chosen so that the boat will land at a point exactly across from its starting point, how long will it Take for the boat to make the crossing? Give your answer to the nearest second.

Determine the number of triangles ABC possible with the given parts. - $a = 24 , b = 21 , A = 47 ^ { \circ }$

Find the dot product for the pair of vectors. - $\langle 7,0 \rangle , \langle 15 , - 3 \rangle$

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

Vector v has the given magnitude and direction. Find the horizontal or vertical component of v, as indicated, if direction angle of v from the horizontal. Round to the nearest tenth when necessary. - $\alpha = 46.7 ^ { \circ } , | \mathbf { v } | = 86.5$ ; Find the horizontal component of $\mathbf { v }$ .

Solve the problem. -It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from the port and its bearing from the lighthouse is N31°E. How far has The ship sailed from the port? Round to the nearest tenth of a kilometer.

Solve the problem. -A plane is heading due south with an airspeed of 245 mph. A wind from a direction of 53° is blowing at 13 mph. Find the bearing of the plane.

Determine whether the pair of vectors is orthogonal. - $\langle 3 , - 9 \rangle , \langle - 6 , - 4 \rangle$

Find the dot product for the pair of vectors. - $\langle 1,18 \rangle , \langle 7,1 \rangle$

Determine the number of triangles ABC possible with the given parts. - $a = 35 , b = 53 , A = 26 ^ { \circ }$

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

Solve the problem. -Two people are carrying a box. One person exerts a force of 129 pounds at an angle of 49.4° with the horizontal. The other person exerts a force of 98 pounds at an angle of 52.4°. Find the weight of The box.

Solve the problem. -A hot-air balloon is rising vertically 10 ft/sec while the wind is blowing horizontally at 4 ft/sec. Find the angle that the balloon makes with the horizontal.

Use the figure to find the specified vector. -Find -a.

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

Determine whether the pair of vectors is orthogonal. - $\langle - 2 , - 1 \rangle , \langle - 16,32 \rangle$

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°]. - $\langle 12 \sqrt { 2 } , - 12 \sqrt { 2 } \rangle$

Solve the problem. -A room in the shape of a triangle has sides of length 14.5 yards, 13.8 yards, and 18.9 yards. If carpeting costs $18.85 per square yard, padding costs $2.40 per square yard, and there is no charge For installation, how much, to the nearest dollar, will it cost to carpet the room?