A parallelogram has sides of length 13.3 cm and 12.5 cm. The longer diagonal has

Question

A parallelogram has sides of length 13.3 cm and 12.5 cm. The longer diagonal has length 24.3 cm. Find the angle opposite the longer diagonal. What is the degree measure of the angle opposite the longer diagonal? (Round to the nearest tenth as needed.) Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force. forces of 327 and 293 newtons, forming an angle of 67 degree The magnitude of the resultant force is newtons. (Round to the nearest newton as needed.) Determine the remaining sides and angles of the triangle ABC. A = 100 degree 50', C = 60 degree 10', AB = 1 BC (Do not round until the final answer. Then round to the nearest hundredth as needed.) AC (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Explanation / Answer

Using cosine law

c2=a2+b2-2abcosC

a= 12.5    b=13.3   and c=24.3

24.32=12.52+13.32-2(12.5)(13.3)cos C

590.49= 333.14- 332.5 cos C

257.35=-332.5cosC

cos C= -(257.35/332.5)

C=cos-1(-257.35/332.5) = 140.7 degree

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