Ch. 4 - Laws of Sines and Cosines; Vectors
Back
- In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 5, b = 7, c = 10
Problem 17
- In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively. a = 30, b = 20, A = 50°
Problem 18
- In Exercises 17–22, find the angle between v and w. Round to the nearest tenth of a degree. v = -3i + 2j, w = 4i - j
Problem 19
- In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-3, 4), P₂ = (6, 4)
Problem 19
- In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 3, b = 9, c = 8
Problem 19
- In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively. a = 57.5, c = 49.8, A = 136°
Problem 20
- In Exercises 17–22, find the angle between v and w. Round to the nearest tenth of a degree. v = 6i, w = 5i + 4j
Problem 21
- In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. u + v
Problem 21
- In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 3, b = 3, c = 3
Problem 21
- In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively. a = 6.1, b = 4, A = 162°
Problem 22
- In Exercises 22–24, sketch each vector as a position vector and find its magnitude. v = -3i - 4j
Problem 22
- In Exercises 23–32, use the dot product to determine whether v and w are orthogonal. v = i + j, w = i - j
Problem 23
- In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. u - v
Problem 23
- In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 63, b = 22, c = 50
Problem 23
- In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively. a = 10, b = 30, A = 150°
Problem 24
- In Exercises 22–24, sketch each vector as a position vector and find its magnitude. v = -3j
Problem 24
- In Exercises 23–32, use the dot product to determine whether v and w are orthogonal. v = 2i + 8j, w = 4i - j
Problem 25
- In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. v - u
Problem 25
- In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit. a = 4 feet, b = 4 feet, c = 2 feet
Problem 25
- In Exercises 25–26, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (2, -1), P₂ = (5, -3)
Problem 25
- In Exercises 25–26, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-3, 0), P₂ = (-2, -2)
Problem 26
- In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively. a = 30, b = 40, A = 20°
Problem 26
- In Exercises 23–32, use the dot product to determine whether v and w are orthogonal. v = 2i - 2j, w = -i + j
Problem 27
- In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. 5v
Problem 27
- In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit. a = 14 meters, b = 12 meters, c = 4 meters
Problem 27
- In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively. a = 7, b = 28, A = 12°
Problem 28
- In Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar. w - v
Problem 28
- In Exercises 23–32, use the dot product to determine whether v and w are orthogonal. v = 3i, w = -4i
Problem 29
- In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. -4w
Problem 29
- In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit. a = 11 yards, b = 9 yards, c = 7 yards
Problem 29