Final answer:
To find the lengths of the other two sides of a 30°-60°-90° triangle with a longest side of 8 cm, we can use the ratios of side lengths in this special triangle.
Step-by-step explanation:
To find the lengths of the other two sides of a 30°-60°-90° triangle, we need to use the ratios of side lengths in this special type of triangle. In a 30°-60°-90° triangle, the ratio of the shorter leg to the longer leg is √3 : 1, and the ratio of the hypotenuse to the longer leg is 2 : 1.
Given that the longest side is 8 cm, we can determine that the longer leg is 8/√3 cm and the shorter leg is (8/√3) * √3 cm. Simplifying these expressions, the longer leg is approximately 4.62 cm and the shorter leg is approximately 8 cm.
Therefore, the lengths of the other two sides of the 30°-60°-90° triangle are approximately 4.62 cm (longer leg) and 8 cm (shorter leg).
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