In a right-angled triangle OMN, the hypotenuse of MH is 15 cm. Find the leg OM if the sine of the angle H is 0.8.

Consider the triangle OMN, MN – hypotenuse, angle C, opposite the hypotenuse <C = 90º, OM and OH – legs, MH = 15 cm, sin H = 0.8.
By definition of the sine of an angle in a right-angled triangle, the sine of an angle is equal to the ratio of the opposite leg angle to the hypotenuse of the triangle:
sin H = OM / MH
From here we express OM:
ОМ = sin H * MH = 0.8 * 15 = 12 cm.
Answer: OM leg is 12 cm.