In a right-angled triangle, one leg is 8 cm, and the sine of the opposite angle is 0.8. Find the hypotenuse and the second leg.

Given: ΔABC – rectangular,
AB = 8 cm, sin (∠C) = 0.8.
Find: BC, AC.
Decision:
Sinus is the ratio of the opposite leg to the hypotenuse.
sin (∠C) = AB / BC;
0.8 = 8 / BC;
BC = 8 / 0.8 = 10 (cm).
By the Pythagorean theorem:
AC ^ 2 = BC ^ 2 – AB ^ 2;
AC ^ 2 = 10 ^ 2 – 8 ^ 2;
AC ^ 2 = 100 – 64 = 36;
AC = 6 (cm).
Answer: AC = 6 cm, BC = 10 cm.