The hypotenuse of a right-angled triangle is 8 cm. Find the leg of this triangle which lies opposite an angle of 60 degrees.

From the school geometry course, we well know that in order to determine the length of the leg, which is opposite a known angle, it will be enough to multiply the length of the hypotenuse and the sine of this angle.

Let’s determine what value the length of the leg will equal, which is opposite an angle of 60 °, when from the condition of our task we know for sure that the length of the hypotenuse in this triangle is 8 centimeters:

sin 60 ° = √3 / 2;

8 * √3 / 2 = 4√3.

Answer: With such initial conditions, it will be equal to 4√3 cm.