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 `12` and the angle between sides B and C is `pi/12`, what is the length of side A?

Answer 1

The three sides are:

`A=3sqrt2(sqrt3+1)`

`B=3sqrt2(sqrt3-1)`

`C=12`

Explanation:

`C=12`

`theta_C=pi/2`

`theta_A=pi/12`

The triangle is a right angled triangle with C as hypotenuse,

Adjacent side `A=Ccostheta_A`

`=12cos(pi/12)`

`cos(pi/12)=(sqrt(3)+1)/(2sqrt2)`

`A=12xx(sqrt(3)+1)/(2sqrt2)=3sqrt2(sqrt3+1)`

`B=Csin(pi/12)`

`sin(pi/12)=(sqrt(3)-1)/(2sqrt2)`

`A=12xx(sqrt(3)-1)/(2sqrt2)=3sqrt2(sqrt3-1)`

The three sides are:

`A=3sqrt2(sqrt3+1)`

`B=3sqrt2(sqrt3-1)`

`C=12`