In triangle abc angle a = 40◦, side b = 11 and side c = 5. use the cosine rule to find the length of side a, to two decimal places. without using the cosine rule again, find the remaining angles b and c, giving your answers to the nearest degree.

Question

Mathematics

Hoover

2 March, 08:20

In triangle abc angle a = 40◦, side b = 11 and side c = 5. use the cosine rule to find the length of side a, to two decimal places. without using the cosine rule again, find the remaining angles b and c, giving your answers to the nearest degree.

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Answers (1)

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Mattie Morse · Answer 1

A^2 = b^2 + c^2 - 2bc cos a

= 11^2 + 5^2 - 2*5*11 cos 40

= 7.86 to 2 DP's

to find the remaining angles use the sine rule:-

a / sin A = b / sin B so

7.857 / sin 40 = 11 / sin B

sin B = 11 sin40 / 7.857 = 0.8999

so