A parallelogram has sides of lengths 8 and 7 and one angle is 36 degrees. What is the length of the smaller diagonal? What is the length of the longer diagonal?

Smaller Diagonal = 4.7

Larger Diagonal = 14.3

Step-by-step explanation:

A parallelogram has sides of lengths 8 and 7 and one angle is 36 degrees. What is the length of the smaller diagonal? What is the length of the longer diagonal?

a) We solve for the smaller diagonal

The formula is given as:

d = √a ² + b² - 2ab Cos A

a = 8, b = 7

d = √8² + 7² - 2 × 8 × 7 × Cos 35

d = √ 113 - 90.60990337

d = √22.39009663

Approximately = 4.7

b) Solving for the larger diagonal

D = √a² + b² + 2ab Cos A

D = √8² + 7² + 2 × 8 × 7 × Cos 36

D = √64 + 49 + 90.60990337

D = √113 +90.60990337

D = √(203.60990336999998)

D = 14.269194209

Approximately = 14.3

answer

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