University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2022
Views:

253

Pages:

5
Author:

SpaceCadet101

Pre-Calc: Laws of Sines/Cosines and Vectors NAME: PERIOD SCORE Draw and label the triangle. Solve each triangle. Round to the nearest hundredth. 1. Given ∠A = 45°, ∠B = 77°, and c = 8 C /| / | / | A___|___B b a sin 45° / a = sin 77° / 8 a = 5.95 sin 58° / b = sin 77° / 8 b = 11.02 2. Given ∠C = 113°, ∠B = 41°, and b = 15 C /| / | / | A___|___B c a sin 113° / c = sin 41° / 15 c = 21.05 sin 26° / a = sin 41° / 15 a = 10.02 3. Given ∠A = 58°, a = 7, and c = 8 C /| / | / | A___|___B b c sin C / 8 = sin 58° / 7 C = 75.74° B = 46.26° sin 46.26° / b = sin 58° / 7 b = 5.74 4. Given ∠A = 39°, b = 21, and c = 15 C /| / | / | A___|___B b c a² = 15² + 21² - 2(15)(21)cos 39° a = 13.28 sin B / 21 = sin 39° / 13.28 B = 84.30° C = 56.64° 5. Given a = 59, b = 77, and c = 83 C /| / | / | A___|___B b c cos C = (59² + 77² - 83²) / (2 * 59 * 77) C = 75.89° sin A / 59 = sin 75.89° / 83 A = 43.07° B = 63.04° 6. Given ∠A = 75°, b = 12, and c = 9, find the area of the triangle rounded to the nearest tenth. 12 /|\ / | \ / | 9 | A = 1/2(9)(12)sin 75° = 52.2 u² / | A_______|_______C b c 7. Given a = 8, b = 10, and c = 5, find the area of the triangle rounded to the nearest tenth. 10 /|\ / | \ / | 8 | A = 1/2(8)(5)sin 97.9° = 19.8 u² / | A_______|_______C b c cos B = (5² + 8² - 10²) / (258) B = 97.9° 8. Given ∠B = 135°, a = 1.2, and c = 3.9, find the area of the triangle rounded to the nearest tenth. b /|\ / | \ / | 1.2 | 3.9 / | A_______|_______C c a A = 1/2(1.2)(3.9)sin 135° = 1.7 u² 9. Given a = 33, b = 26, and c = 41, find the area of the triangle rounded to the nearest tenth. b /|\ / | \ / | 33 | 41 / | A_______|_______C c a cos B = (26² + 33² - 41²) / (22633) B = 98.4° A = 1/2(20)(33)sin 98.4° = 326.5 u² 10. Find the (a) component form and (b) magnitude of vector v, if vector v has an initial point at (0, 0) and terminal point at (-5, 12). a) <-5, 12> b) √((-5)² + 12²) = √169 = 13 11. Find the (a) component form and (b) magnitude of vector v, if vector v has an initial point at (-2, 3) and terminal point at (-9, -4). a) <-9 - (-2), -4 - 3> = <-7, -7> b) √((-7)² + (-7)²) = √98 = 7√2