Question

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?

Answer 1

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

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