A triangle has sides A, B, and C. If the angle between sides A and B is #(pi)/8#, the angle between sides B and C is #(pi)/3#, and the length of B is 2, what is the area of the triangle?

1 Answer
bp
May 10, 2016

Area= 0.6685

Explanation:

The triangle ABC and its given components would be as shown in the figure. Angle B= #pi- pi/3-pi/8= (13pi)/24#. apply sine law to find side a or side c. Let us get a
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a = #2sin (pi/3)/ sin ((13pi)/24)#

To find the area length of perpendicular fro B upon side b is required . It would be a #sin (pi/8)#

Area= #(1/2) (2) # a #sin (pi/8)#

= a #sin (pi/8)# = #2 sin(pi/3) /sin(13pi/24) sin (pi/8)#

=0.6685

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