Question

15. (-/1 Points)Find the remaining sides of a 30°-60°-90° triangle If the longest side is 3. (Enter your answers as a comma-separated list.) 16. (0/1 Points) Find the remaining sides of a 30°-60°-90 triangle in the side opposite 60° is 12. (Enter your answers as a comma-separated list.) √48

Answer 1

For a 30°-60°-90° triangle, if the longest side (hypotenuse) is 3, the remaining sides are 1.5 and ~2.598. If the side opposite 60° is 12, the remaining sides are ~6.928 and ~13.856.

Step-by-step explanation:

In a 30°-60°-90° triangle, the sides are proportionally related. The side across from the 30° angle is half the length of the hypotenuse, and the side across from the 60° angle is the length of the hypotenuse multiplied by √3 divided by 2. For the first example, the remaining sides would be 3/2 for the side across from 30°, and 3*√3/2 for the side opposite the 60°, which equals 1.5 and ~2.598, respectively. In the second example, if the side opposite 60° is 12, then the hypotenuse would be twice the length of the side across from 30°. Hence, it would be 12*2/√3, or ~13.856. The shortest side (across from 30°) would be half of the hypotenuse, or ~6.928.

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