Final answer:
In a right angled triangle, if one of the acute angles is 30 degrees and its opposite side has a length of 8 cm, the length of the hypotenuse can be found using trigonometric ratios. The length of the hypotenuse is 16 cm.
Step-by-step explanation:
In a right angled triangle, if one of the acute angles is 30 degrees and its opposite side has a length of 8 cm, we can use trigonometric ratios to find the length of the hypotenuse. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the sine of 30 degrees can be written as:
sin(30) = 8 / hypotenuse
We can rearrange the equation to solve for the hypotenuse:
hypotenuse = 8 / sin(30)
Using a calculator, we can find that sin(30) is approximately 0.5. Substituting this value into the equation, we get:
hypotenuse = 8 / 0.5 = 16 cm
Therefore, the length of the hypotenuse is 16 cm.