7. Non-Right Triangles

In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit.a = 2 meters, b = 2 meters, c = 2 meters

Use one or more of the six sum and difference identities to solve Exercises 13–54.In Exercises 13–24, find the exact value of each expression.cos(135° + 30°)

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

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

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

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

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

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

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

In Exercises 35–38, find the exact value of the following under the given conditions:βe. cos -------23 𝝅 12 𝝅 sin α = ------- , 0 < α < -------- , and sin β = --------- , --------- < β < 𝝅. 5 2 13 2

In Exercises 35–38, find the exact value of the following under the given conditions:b. cos(α﹣β)3 𝝅 12 𝝅 sin α = ------- , 0 < α < -------- , and sin β = --------- , --------- < β < 𝝅. 5 2 13 2

In Exercises 35–36, the three given points are the vertices of a triangle. Solve each triangle, rounding lengths of sides to the nearest tenth and angle measures to the nearest degree.A(0, 0), B(-3, 4), C(3, -1)

In Exercises 35–38, find the exact value of the following under the given conditions:βe. cos -------21 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2

In Exercises 35–38, find the exact value of the following under the given conditions:b. cos(α﹣β)1 3𝝅 1 3𝝅 sin α =﹣ ------ , 𝝅 < α < ------- , and cos β =﹣------ , 𝝅 < β < ---------. 3 2 3 2

In Exercises 57–64, find the exact value of the following under the given conditions:a. cos (α + β)3 5sin α = ------ , α lies in quadrant I, and sin β = ------- , β lies in quadrant II.5 13