A triangle has sides A, B, and C. If the angle between sides A and B is (5pi)/8, the angle between sides B and C is (pi)/3, and the length of B is 16, what is the area of the triangle?

1 Answer
LM ยท Shwetank Mauria
Nov 9, 2017

784.42 square units (2 d.p.)

Explanation:

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A = 1/2ab sin C
this formula can be used when working with 2 sides and 1 angle - a and b are the two sides that are not opposite the angle we are using.

however, there is only 1 side given, so we need to find a second side - either a or c.

first, find the angle between a and c:

Sigma_angle(triangle) = pi

angle between a and c = pi - ((5pi)/8) - (pi/3)

= pi/24

sine rule: a/sin A = b/sin B = c/sin C

16/sin(pi/24) = a/sin(pi/3)

16sin(pi/3)=asin(pi/24)

16xx0.86603=0.13053a

a=(16xx0.86603)/0.13053=

a = 106.16, b = 16

angle opposite c =(5pi)/8

"Area"=1/2(106.16*16)sin(5pi)/8

=849.028xx0.9239

"Area" = 784.42 square units (2 d.p.)

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