Complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.)

Question

a = ____

b = 24

c = 53

d = 37

𝜃 = ____ °

𝜑 = ____ °

Answer 1

c² + d² = 2a² + 2b²; 53² + 37² = 2a² + 2·24²; a² = 1513; a = 38.90;

By cosine law: d² = a² + b² - 2abcosθ; cosθ = (1513 + 576 - 37²)/(2·38.9·24) = 0.3856; θ = cos^-10.3856) = 67.3°; φ = 180° - 67.3° = 112.7°

Answer 2

Detailed instructions to complete this problem have been presented multiply times.