Question - Calculating side lengths of a 30-60-90 triangle
Solution:
The image shows a right-angled triangle with one angle marked as 30 degrees and the side opposite to this angle is given as 6. In a right-angled triangle where one of the angles is 30 degrees, we can apply the special right triangle ratios that hold true for 30-60-90 triangles.In a 30-60-90 triangle, the ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles is 1:√3:2, respectively.Since the side opposite the 30° angle (the shortest side) is given as 6, we can determine the lengths of the other sides using the ratio:- The length of the hypotenuse (opposite the 90° angle) is twice the length of the side opposite the 30° angle. So, the hypotenuse = 2 × 6 = 12.- The length of the side opposite the 60° angle (the longer leg) is √3 times the length of the side opposite the 30° angle. So, the longer leg = √3 × 6 = 6√3.In summary, the lengths of the sides of the triangle are:- Shortest side (opposite 30°): 6- Longer leg (opposite 60°): 6√3- Hypotenuse (opposite 90°): 12These are the side lengths of the triangle based on the given information.
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