Unit Test Answers

Given vectors u = ⟨–2, 3⟩ and v = ⟨–6, 9⟩, what is the measure of the angle between u and v?

Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet.Trigonometric area formula: Area =

Review the graph.

A force of 50 pounds acts in a direction 60° above horizontal, moving an object 100 feet from (0, 0) to (100, 0). How much work is done by the force?

Review the graph.

Triangle XYZ has vertices X(–1, –1), Y(–2, 1), and Z(1, 2). What is the approximate measure of angle Z?

A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components . After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station.What are the characteristics of the vector representing the path of the ship?

Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?

Trigonometric area formula: Area =

A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?

After a windstorm, a leaning pole makes a 75° angle with the road surface. The pole casts a 15-foot shadow when the sun is at a 45° angle of elevation. About how long is the pole?

Let a = 2i + 9j, b = –4i + 5j, c = i – 3j, and d = 14j where i and j are unit vectors. What is (a – b) – (2d – c) in terms of i and j?

Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?

A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?

Let |u| = 4 at an angle of 210° and |v| = 9 at an angle of 315°, and w = u – v. What is the magnitude and direction angle of w?

In triangle ABC, AB = 90 in., BC = 80 in., and angle B measures 50°. What is the approximate perimeter of the triangle?

What are the possible remaining angle measures in triangle ABC with ?

Which diagram shows the parallelogram method for vector addition?

Let u =. What is 3u?

Review the diagram.

The magnitude of vector u is 34, and the magnitude of vector v is 20. The dot product u · v = –10. What is the approximate angle between the vectors?

The speed of a boat in still water is 25 mph. The boat is traveling on a river with a current flowing south at 10 mph. At what angle upstream should the boat head to travel due west?

A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.Heron’s formula: Area =

A vector has initial point at (3, –5) and terminal point at (–2, 3). What are the characteristics of this vector?

A plane took off at a 15° angle to the ground and flew in Sydney’s direction. She is standing at a point 25 miles from the point where the plane took off. If the plane has traveled 20 miles in the air, about how far is Sydney from the airplane? Round your answer to the nearest whole number.