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Determine the length of the long leg of a 30-60 right triangle if the short side is 4.4 . (Round answers to nearest tenth.)​

Determine the length of the long leg of a 30-60 right triangle if the short side is-example-1

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Final answer:

To find the length of the long leg of a 30-60-90 triangle with a short leg of 4.4, multiply 4.4 by √3 (≈ 1.732), resulting in approximately 7.6 when rounded to the nearest tenth.

Step-by-step explanation:

To determine the length of the long leg of a 30-60-90 right triangle when the short side is 4.4, we apply the knowledge that the ratio of the sides in a 30-60-90 triangle is 1:√3:2. The short leg corresponds to '1' in this ratio, representing the shortest side, opposite the 30° angle. The long leg, opposite the 60° angle, corresponds to '√3' in the ratio. Since the short leg has a length of 4.4, we calculate the long leg (L) using the ratio:

L = short leg × √3

L = 4.4 × √3

L ≈ 4.4 × 1.732

L ≈ 7.6208

When rounded to the nearest tenth, the length of the long leg is approximately 7.6.

User Thiago Jackiw
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