In the OMT triangle, the angle is T = 60 degrees, OT = 6, OM = 12. Find the sine of the angle M.

To solve the problem, you need to remember the theorem of sines: the sides of a triangle are proportional to the sines of the opposite angles.

a / sinα = b / sinβ = c / sinγ.

Having an angle T = 60 ° and two sides: OT = 6 cm, OM = 12 cm, you can add the proportion in order to find sin∠M.

ОМ / sin∠Т = OT / sin∠М.

12 / sin∠60 ° = 6 / sin∠M.

sin∠M = sin∠T x OT / OM = √3 / 2 x 6/12 = 3√3 / 12 = √3 / 4.

Answer: sin∠М = √3 / 4.