6ab please and thank u 6 Use the Law of Cosines to find the

6. Use the Law of Cosines to find the unknown sides b) D 10.5 cm 11 cm 13 cm 9.5 cm MacBook Air S D F G H J K L

Solution

6 a)

applying law of cosines

b^2 = a^2 + c^2 - 2ac cos (B)

plugging the values

b^2 = 10.5^2 + 9.5^2 - 2(10.5)(9.5) cos 40

b = 6.9

therefore length of AC = 6.9 cm

b) again applying law of cosines

e^2 = f^2 + d^2 - 2fd cos 75

e^2 = 13^2 + 11^2 - 2(13)(11) cos 75

e = 14.7 cm

4a) applying law of sines to find the value of x

a / sin A = b/ sin B

90/ sin 90 = x / sin 50

90 / 1 = x / sin 50

x = 90 * sin 50

x = 68.94 mm

b) again applying law of sines

x / sin 51 = 30 / sin 39

x = 30/ sin 39 * sin 51

x = 37.05 cm