Answer:
shorter leg = 8
longer leg = 8√3
Explanation:
If the hypotenuse of the 60-90-30 triangle is 16, we can use the ratios of the sides to find the lengths of the other two sides. Here's how we can solve for the missing sides:
The length of the shorter leg (opposite the 60-degree angle) is half the length of the hypotenuse:
shorter leg = (1/2) * hypotenuse
= (1/2) * 16
= 8
The length of the longer leg (opposite the 30-degree angle) can be found using the ratio of the sides in a 30-60-90 triangle:
longer leg = shorter leg · √3
= 8√3
So, the missing side of the triangle are 8 and 8√3