## anonymous one year ago 30-60-90 triangle question

1. TheSmartOne

Post away

2. anonymous

3. anonymous

@thesmartone

4. anonymous

@happyrosy

5. anonymous

@Nnesha

6. anonymous

This is more properties of a 30-60-90 triangle than Pythagorean theorem.

7. TheSmartOne

Do you know the relationship of sides of a 30-60-90 triangle?

8. anonymous

YES

9. TheSmartOne

Can you draw it using the draw tool?

10. anonymous

ok i already know the answer and it showed me it but can you explain how the answer was worked out?

11. anonymous

12. TheSmartOne

|dw:1433881486021:dw|

13. anonymous

ok, but i don't know how to solve it

14. TheSmartOne

They gave you the side opposite the right angle as $$\sf 8\sqrt{3}$$ And so if we look at the drawing I posted, and correlate the sides to solve for a we get: $$\sf 2a = 8\sqrt{3}$$ $$\sf\Large a=\frac{8\sqrt{3}}{2}=4\sqrt{3}$$

15. TheSmartOne

and you can see that the side that they want is the side opposite the angle 60 In the drawing I posted, it has a value of $$\sf a\sqrt{3}$$ and we calculated a as $$\sf 4\sqrt{3}$$ So if we plug in the value of a, we get: $$\sf 4 \sqrt{3}\times \sqrt{3}=4 \times 3 = 12$$

16. anonymous

The side opposite 30 degrees is always half of the hypotenuse. So if the hypotenuse is $8\sqrt{3}$ then the side opposite to the 30 degees would be $\frac{8\sqrt{3}}{2}$ which is $4\sqrt{3}$ And the 60 degrees side is always the 30 degrees side times sqrt 3. So it would be $4\sqrt{3}*\sqrt{3}$ which is the same as $4\sqrt{9}$ which is $4*3$ which obviously get you 12.