Question

drag each length to the correct location on the triangle. each length can be used more than once, but not all lengths will be used.
what are the missing side lengths for triangle abc?
4 (8sqrt{3}) (4sqrt{2}) 12 (8sqrt{2}) 8 (4sqrt{3})
triangle with 30°, 60°, right angle, and one leg (4sqrt{3})

Explanation:

Step1: Identify triangle type & sides

This is a 30-60-90 right triangle. Let:

• Side opposite 30°: $x$
• Side opposite 60°: $4\sqrt{3}$ (given)
• Hypotenuse: $2x$

Step2: Solve for $x$ (opposite 30°)

In 30-60-90 triangles, side opposite 60° = $x\sqrt{3}$.
$$x\sqrt{3}=4\sqrt{3}$$
$$x=4$$

Step3: Solve for hypotenuse

Hypotenuse = $2x$
$$2x=2\times4=8$$

Answer:

The missing side lengths are 4 (opposite the 30° angle) and 8 (the hypotenuse).