In a right-angled triangle, the legs are 4 cm and 4√3 cm. Find the hypotenuse and the larger acute angle.

Let us determine how long the hypotenuse will be in a right-angled triangle, when from the condition of the task we know that the length of one leg is 4 centimeters, while the length of the other is 4√3 centimeters:

√ (4 ^ 2 + (4√3) ^ 2) = √ (16 + 48) = √64 = 8.

As we know from the school geometry course, on the contrary, the larger the side will be the larger angle.

Determine what the sine of the angle will be equal to, which lies opposite the side at 4√3:

4√3: 8 = √3 / 2.

This is a 60 ° angle:

Answer: The angle is 60 °, and the hypotenuse is 8 cm.