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

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

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

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]( useruploads.socratic.org )

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.

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