## 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. hwyl

how do you know that this is easy?

3. hwyl

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. hwyl

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

7. hwyl

longer leg is always across the 60 angle

8. anonymous

certainly hypotenuse is longest .

9. hwyl

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

10. hwyl

|dw:1443135576185:dw|

11. hwyl

|dw:1443135732498:dw|

12. hwyl

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

13. hwyl

|dw:1443136114788:dw|

14. hwyl

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

15. hwyl

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

16. hwyl

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

17. hwyl

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