Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/2` and the angle between sides B and C is `pi/12`. If side B has a length of 45, what is the area of the triangle?

Answer 1

271.299

Explanation:

the angle between A and B = `Pi/2` so the triangle is a right-angled triangle.

In a right-angled triangle, the tan of an angle = `(Opposite)/(Adjacent)`

Substituting in the known values
`Tan (Pi/2) = 3.7320508 = 45/(Adjacent)`

Rearranging and simplifying
`Adjacent = 12.057713`

The area of a triangle = `1/2*base*height`

Substituting in the values
`1/2*45*12.057713 =271.299`