A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2#. If side C has a length of #1 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2018-03-25T12:04:52

#color(green)(c = (1 sin (pi/12) ) / 1 = sin (pi/12) = 0.2588 " units"#

#hat C = pi/2, c = 1, hat A = pi/12, " To find a#

Applying Law of Sines,

#a /Sin A = c / sin C#

#a = (c * sin A) / sin C = (1 * sin (pi/12) ) / sin (pi/2)#

#color(green)(c = (1 sin (pi/12) ) / 1 = sin (pi/12) = 0.2588 " units"#

#Verification : "#

#hat B = pi - pi/2 - pi/12 = (5pi)/12#

#b = (1 * sin ((5pi)/12))/sin (pi/2) = sin (5pi)/12 = 0.966#

#a^2 + b^2 = 0.2588^2 + 0.966^2 = 1 = c^2#

Since it's a right triangle, #c ^2 = a^2 + b^2#

Hence proved.