In a right triangle, one of the legs is 4 cm, and the sine of the opposite angle is 0.8.

In a right triangle, one of the legs is 4 cm, and the sine of the opposite angle is 0.8. Find its second leg, the hypotenuse of this triangle.

It is known that in any right-angled triangle the length of the leg is equal to the product of the length of the hypotenuse of this triangle by the sine of the opposite angle.

Suppose the length of the hypotenuse of this triangle is x.

We get the equation:

0.8 * x = 4,

x = 4: 0.8,

x = 5 (cm) – the length of the hypotenuse.

Now we can find the length of the second leg using the Pythagorean theorem. Let’s denote the length of the unknown leg by the letter y and get:

4² + y² = 5²,

16 + y² = 25,

y² = 25 – 16,

y² = 9,

y = 3 (cm) – the length of the second leg.