Question - Calculating Side Lengths of a 30-60-90 Triangle
Solution:
The image shows a right-angled triangle with one angle of 30 degrees, indicating that this is a 30-60-90 triangle, a special type of right triangle. The side opposite the 30-degree angle, the shortest side, is labeled as 6 units in length.In a 30-60-90 triangle, the lengths of the sides are in a consistent ratio. The side opposite the 30-degree angle (the shortest side) is typically labeled as 'x'. The side opposite the 60-degree angle (the longer leg) is '√3 * x', and the side opposite the 90-degree angle (the hypotenuse) is '2x'.Given that the shortest side is 6 units (x = 6), we can find the lengths of the other two sides as follows:- The longer leg (60-degree side) = √3 * x = √3 * 6 = 6√3- The hypotenuse (90-degree side) = 2x = 2 * 6 = 12So, the side opposite the 60-degree angle is 6√3 units long, and the hypotenuse is 12 units long.
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