## anonymous one year ago Trigonometry help, easy medal and fan

1. anonymous

the longer leg of a 30-60-90 triangle is 18. what is the length of the other leg

2. anonymous

how do you know that this is easy?

3. anonymous

there are two ways to solve this problem

4. anonymous

|dw:1443145786138:dw| you can also solve it by trigonometry.

5. anonymous

Ey yo thanks!

6. anonymous

it says the longer leg, so I am not sure if that pertains to the hypotenuse

7. anonymous

longer leg is always across the 60 angle

8. anonymous

certainly hypotenuse is longest .

9. anonymous

that would be the LONGEST, but the problem says LONGER so we can make it this way long, longer and longest

10. anonymous

|dw:1443135576185:dw|

11. anonymous

|dw:1443135732498:dw|

12. anonymous

$$longleg = y^2 = 2^2 - 1^2 \rightarrow y = \sqrt{3}$$

13. anonymous

|dw:1443136114788:dw|

14. anonymous

based on these information, without the use of trigonometry, we can use patterns $$shortleg = \frac{1}{2}hypotenuse$$

15. anonymous

if shortleg is 1/2 of hypotenuse then $$longleg = shortleg \times \sqrt{3}$$

16. anonymous

or $$longleg = \frac{1}{2}hypotenuse \times \sqrt{3}$$

17. anonymous

$$(18 \times 2) \div \sqrt{3} = hypotenuse$$ becase we know that: $$shortleg = \frac{1}{2}~ hypotenuse$$