Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/6` and the angle between sides B and C is `pi/6`. If side B has a length of 5, what is the area of the triangle?

Answer 1

`Area=(25sqrt3)/12=3.60844` square units

Explanation:

The triangle is isosceles. The base angles `A=pi/6=30^@` and `B=pi/6=30^@`. We can readily see that `1/2` of the base `b` equal `5/2`. Use `5/2` to compute side `c`.

`Cos (pi/6)=(5/2)/c`

`c=(5/2)/cos (pi/6)=(5/2)/(sqrt(3)/2)=5/sqrt3=(5sqrt3)/3`

Compute the Area now using the formula for two sides and an included angle

`Area=1/2*b*c*sin A`

`Area=1/2*5*(5sqrt3)/3*sin (pi/6)`

`Area=1/2*5*(5sqrt3)/3*1/2`

`Area=(25sqrt3)/12=3.60844` square units

Have a nice day!!! from the Philippines