Consider a 30∘−60∘−90∘ triangle when the long side is 8.

Question

I couldn't figure this problem out, I need help please!

Answer 1

You failed to ask a question!

What are the sides of the 30-60-90 triangle you memorized. What do you have to multiply the longest side by to get 8. Multiply all sides by that number.

Answer 2

In a 30° - 60° - 90° triangle, the sides are can be determined in formulas. The side across from the 30° is the smallest side which will contain the value s. The side across from the 60° angle is the middle in length and it has a value of s multiplied by √3 which is written as s√3. The final side is the one across from the 90° which is the longest and called the hypotenuse. It has the value of s times 2 which will be written 2s.

Therefore if the hypotenuse is of length 8 we know that

8 = 2s

and then we can divide both sides by 2 so that

4 = s

which is now the length of our shortest side. Finally, to calculate the middle side we can multiply by √3 to give 4√3.

I hope that helps give direction for you problem.

Answer 3

The longest side is the side opposite the largest angle. So, the hypotenuse has length 8.

In a 30° - 60° - 90° triangle, the side opposite the 30° angle is half the length of the hypotenuse and the side opposite the 60° angle is √3 times as long as the side opposite the 30° angle.

So, the side opposite the 30° angle has length 4 and the third side has length 4√3.