Answer:
A 30-60-90 triangle is a special type of right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The side opposite the 30 degree angle is called the "short leg", the side opposite the 60 degree angle is called the "medium leg", and the side opposite the 90 degree angle is called the "long leg".
The ratios of the sides in a 30-60-90 triangle are always in the proportion of 1 : √3 : 2 . To find the legs of a 30-60-90 triangle when given the long leg, you can use these ratios.
If the long leg is "x", then the short leg is x/2 and the medium leg is x*√3/2.
For example, if the long leg is 8 cm, you can use these ratios to find the short leg and medium leg:
The short leg is 8 cm / 2 = 4 cm
The medium leg is 8 cm * √3 / 2 = 4 * √3 cm = 4 * 1.732 cm = 6.928 cm (approx)
So, in this example, the short leg is 4cm and the medium leg is 6.928cm (approx).
It's always a good idea to draw a diagram and label the sides to help you visualize the problem and check your answer.
Explanation: