Question

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?

Answer 1

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

Explanation:

`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.