## A community for students. Sign up today

Here's the question you clicked on:

## Babynini one year ago Two wires tether a balloon to the ground as shown, how high is the balloon above the ground? I've done it twice..

• This Question is Closed
1. Babynini

|dw:1434516280906:dw|

2. Babynini

@sdfgsdfgs

3. Babynini

@mukushla

4. Babynini

|dw:1434516477919:dw|

5. Babynini

is that correct?

6. Babynini

@zepdrix :)

7. Babynini

@rational

8. Babynini

the answer I keep getting for height = 371.78 but that's not correct o.0

9. kropot72

|dw:1434517128031:dw| I would solve it this way: $\large \tan 75=\frac{h}{100+x}\ ..........(1)$ $\large \tan 85=\frac{h}{x}\ .........(2)$ Rearranging (2) we get: $\large x=\frac{h}{\tan 85}\ ..........(3)$ Plugging the value for x from (3) into (1) gives: $\large \tan 75=\frac{h}{100+\frac{h}{\tan 85}}\ ..........(4)$ Now solve (4) to find the value of h.

10. kropot72

Equation (4) rearranges to give: $\large 100 \tan 75 +\frac{h \tan 75}{\tan 85}=h\ ..........(5)$ Can you solve h?

11. Babynini

Um.. 373.205+ (htan(75))/11.43

12. Babynini

How do I solve for h if h is in the left side as well?

13. kropot72

Putting values into (5) we get: $\large 373.2+0.3265h=h\ ........(6)$ Subtracting 0.3265h from both sides gives: $\large 0.6735h=373.2\ ..........(7)$

14. Babynini

You mean 0.6735h= - 373.2 (notice this side is negative)

15. Babynini

How did you get 0.6735?

16. kropot72

No, 373.2 is not negative. $\large \frac{h \tan 75}{\tan 85}=0.3265h$

17. Babynini

sorry, I got lost on part 7 We have 373+0.32658h=h (6) if we subtract 0.32658h from both sides we would get 373=h-0.32658h

18. kropot72

373=h-0.32658h 1.00000h -0.32658h=?

19. Babynini

Ah, gotcha. Ok :P

20. kropot72

Cool!

21. Babynini

So now we divide 373 by 0.6735

22. kropot72

Correct.

23. Babynini

and get 554, which is the correct answer :P

24. Babynini

what was I doing that was wrong?! o.o

25. kropot72

You needed to form a pair of simultaneous equations to solve this question. Notice I added another variable x to the drawing. Of course we do not need to find the value of x (although we could by substitution).

26. Babynini

Right, I used tan first and then used the Law of Sines..

27. kropot72

Your equation tan (theta) = y/100 is not understood by me. Where is y in the drawing?

28. Babynini

ai, I meant tan(theta)=x/100

29. Babynini

|dw:1434519774006:dw| tan(75)=x/100 100tan75)=373.205 Then I did the law of sines a/(sin85) = x/sin90 a= (xsin85)/(sin(90)) so the height = 371.78

30. Babynini

The equation for finding the x? to use tangent It needs to be a right triangle?

31. kropot72

The triangle with x, 75 degrees and a side length of 100 units is not a right angled triangle. Therefore your equation is not valid.

32. kropot72

In your usage of tan in a triangle, the triangle must be a right-angled type.

33. Babynini

oh gosh, I didn't know that. That's really good to know o.0

34. kropot72

You're welcome :)

35. Babynini

ok, thanks :)

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy