Find the missing values by solving a parallelogram.(The lengths of the diagonals are given by c and d. Round your answers to two decimal places.)

Question

Find the missing values by solving a parallelogram. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.)

a = ____

b = 21

c = 42

d = 38

𝜃 = ____ °

𝜑 = ____ °

Answer 1

a² = (c² + d²)/2 - b² = (42² + 38²)/2 - b² = 1163; a = √1163 = 34.10;

By cosine law 42² = 21² + 34.10² - 2·21·34.10cosθ; cosθ = (21² + 34.10² - 42²)/(2·21·34.10) = - 0.11185;

θ = 96.42°; φ = 180° - 96.42° = 83.18°