## Abbie23 3 years ago From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 57°, as shown below. If the height of the balloon is 15 miles, what is the distance between the radio antenna and the library?

1. SmoothMath

Howdy.

2. SmoothMath

|dw:1336435993255:dw| Is this right?

3. SmoothMath

What is wrong?

4. Abbie23

|dw:1336436127388:dw|

5. SmoothMath

Oooh. Cool. Got it.

6. SmoothMath

Alright, so the first step is to figure out which trig function is worth using. To figure this out, I like to find where the angle I know is and then label my sides opposite, adjacent, and hypotenuse.

7. SmoothMath

You know which side is which?

8. Abbie23

The hypotenuse is the opposite side of 15 miles and the adjacent side is...have no idea?

9. SmoothMath

|dw:1336436548036:dw|

10. SmoothMath

Cool? The 15 miles side is adjacent to the angle we know. The x side is opposite from that angle. The hypotenuse is always the long side, the one opposite from the right angle.

11. Abbie23

Well I got the hypotenuse side right :) Okay got the other sides, thanks!

12. DoomDude

1 sec...

13. DoomDude

I am not really sure, I am not good at geometry, would you like me to try to get someone else here?

14. DoomDude

sorry, but do you want me to try to get someone that know it here?

15. Abbie23

It's okay :) You don't have to do that! Haha I'll just guess :)

16. DoomDude

no! wait, let me get someone

17. DoomDude

@amistre64 @lgbasallote @imranmeah91 @LagrangeSon678 @AccessDenied

18. SmoothMath

Mildly obnoxious, bro. lols.

19. DoomDude

it works...

20. SmoothMath

Abbie, the side you know is adjacent. The side you need to know is opposite. See that? Which trig function involves opposite and adjacent?

21. Abbie23

Oh okay I see that. And tangent!

22. lgbasallote

uhmm im assuming no help necessary anymore?

23. DoomDude

I am pretty sure that it is... Is it abbie?

24. SmoothMath

Yes, it's tangent. Write an equation using tangent. Tan(57) = opposite/adjacent = x/15 solve for x

25. Abbie23

Yeah, I think so too @Drake Thank you for helping me :)

26. Abbie23

Thanks @SmoothMath :)

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