## Babynini one year ago Height of a mountain To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32 degrees. One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 35 degrees. Estimate the height of the mountain.

1. Babynini

|dw:1434728278112:dw|

2. Babynini

@rvc free?

3. Babynini

@zepdrix :)

4. Babynini

@Michele_Laino

5. Babynini

(the drawing was not given to me, it is my representation of the question)

6. Michele_Laino

I think that the right drawing is: |dw:1434728792636:dw|

7. Babynini

hrrm, ok. I thought of that but didn't want to assume it was a right angle.

8. Babynini

|dw:1434728933190:dw|

9. Babynini

right?

10. Michele_Laino

yes! correct!

11. Michele_Laino

then: h= x * tan(32)

12. Michele_Laino

oops: h= x* tan(35)

13. Babynini

Hm? why that? that's the second triangle

14. Babynini

you mean after we solve for x in tan(32) = h/(1000+x) then we do h= x*tan(35) ??

15. Michele_Laino

yes! |dw:1434729130312:dw|

16. Michele_Laino

we have the subsequent step: $\begin{gathered} \left( {x + 1000} \right)\tan 32 = h = x\tan 35 \hfill \\ \hfill \\ \left( {x + 1000} \right)\tan 32 = x\tan 35 \hfill \\ \end{gathered}$

17. Michele_Laino

we have to solve the last equation for x

18. Babynini

er well 1,000tan(32) = 624.87

19. Michele_Laino

ok! correct!

20. Michele_Laino

$x\tan 32 + 624.87 = x\tan 35$

21. Babynini

So why does that equal xtan35?

22. Babynini

and not h

23. Michele_Laino

since you don't know the value of x

24. Babynini

hm k. Now what do we do? :)

25. Michele_Laino

we have to subtract x*tan(32) from both sides, so we get: $\begin{gathered} 624.87 = x\tan 35 - x\tan 32 \hfill \\ \hfill \\ 624.87 = x\left( {\tan 35 - \tan 32} \right) \hfill \\ \end{gathered}$

26. Michele_Laino

then dividing both sides by (tan35-tan32), we get: $x = \frac{{624.87}}{{\tan 35 - \tan 32}} = ...$

27. Babynini

8294.19 !

28. Babynini

ft

29. Michele_Laino

ok! Now substitute that value into this formula: $h = 8294.2 \times \tan 35 = ...$

30. Michele_Laino

since: $h = x\tan 35$

31. Babynini

I plug it into that second one?

32. Babynini

= 5807.7 ft

33. Michele_Laino

that's right!

34. Babynini

yayaya :)

35. Michele_Laino

:)

36. Babynini

So what we did: tan(32) = h/(1000+x) (1000+x)tan(32)=h xtan32+625.87 = xtan(35) subtract xtan(32) from both sides 625.87 = xtan(35)-xtan(32) 625.87 = x(tan(35)-tan(32)) divide the 625 by the tans to get x = 8294 plug that into h=xtan(25) to get our result 5808ft

37. Michele_Laino

that's right, nevertheless it is 624.87 not 625.87

38. rvc

Thank you so much @Michele_Laino :)

39. Michele_Laino

:) @rvc

40. Babynini

Oh, right. Sorry, that was a typo :P thanks!!

41. Michele_Laino

thanks!!