waheguru
  • waheguru
A bridge across a valley is 150 m in length. The valley walls make angles of 60 degrees & 54 degrees with the bridge that spans it. How deep is the valley, to the nearest metre
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SOLVED
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katieb
  • katieb
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waheguru
  • waheguru
Please Help Me With This Question, I ave been trying for quiet a long time and I am getting the wring answer
Mertsj
  • Mertsj
quite not quiet
waheguru
  • waheguru
Sorry

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More answers

waheguru
  • waheguru
How Do I solve this?
waheguru
  • waheguru
|dw:1370304754446:dw|
Mertsj
  • Mertsj
|dw:1370304738383:dw|
waheguru
  • waheguru
|dw:1370304814686:dw|
waheguru
  • waheguru
Above, is how the question diagram is
Mertsj
  • Mertsj
\[\frac{\sin 66}{150}=\frac{\sin 60}{x}\]
waheguru
  • waheguru
What do i do from here?
Mertsj
  • Mertsj
x=142.2
waheguru
  • waheguru
We are supposed to find the depth
waheguru
  • waheguru
|dw:1370304930976:dw|
waheguru
  • waheguru
|dw:1370304960496:dw|
Mertsj
  • Mertsj
|dw:1370304905792:dw|
Mertsj
  • Mertsj
Should have found y. Don't really need that other side.
waheguru
  • waheguru
Can I show the steps I took, because I really want to know where I am going wrong
Mertsj
  • Mertsj
\[\frac{\sin 66}{150}=\frac{\sin 54}{y}\]
Mertsj
  • Mertsj
Sure
Mertsj
  • Mertsj
y=132.8
waheguru
  • waheguru
|dw:1370305158896:dw|
Mertsj
  • Mertsj
|dw:1370305170408:dw|
waheguru
  • waheguru
|dw:1370305271869:dw|
Mertsj
  • Mertsj
|dw:1370305235905:dw|
waheguru
  • waheguru
The Way I did it was that I split it in to two triangles and Isolated how long the bridge would be for each triangle then I used the tangent to find the depth of the triangle
dumbcow
  • dumbcow
that would work as well, using that method you should end up with \[h = \frac{150 \tan(60) \tan(54)}{\tan(60) +\tan(54)}\]
Mertsj
  • Mertsj
So you said: \[\tan 60=\frac{h}{x} and \tan 54=\frac{h}{150-x}\]
dumbcow
  • dumbcow
there is more than 1 correct way of doing this problem :)
waheguru
  • waheguru
|dw:1370305424647:dw|
Mertsj
  • Mertsj
Ok. dumbcow will help you now...too many cooks... you know what I mean?
waheguru
  • waheguru
@Mertsj Plkease Help Me, I realy need your help
waheguru
  • waheguru
So I tried solving it the above way but im getting 207 for some reason
waheguru
  • waheguru
|dw:1370305743168:dw|
dumbcow
  • dumbcow
@waheguru , so you solved for x right? why not just solve for e right way? \[\tan(30) e = 150 - \tan(36)e\]
waheguru
  • waheguru
@dumbcow I understand, but our teacher expects it by solving for x and then e. We have a test comming up and I really want to know how to do it
Mertsj
  • Mertsj
so: \[\frac{x}{\tan 30}=\frac{150-x}{\tan 36}\]
waheguru
  • waheguru
Yes
Mertsj
  • Mertsj
Is that the equation you wrote?
waheguru
  • waheguru
Yea
Mertsj
  • Mertsj
Did you cross multiply?
waheguru
  • waheguru
Yea
Mertsj
  • Mertsj
\[x \tan 36=(150-x)\tan 30\]
waheguru
  • waheguru
yep
Mertsj
  • Mertsj
\[.7265x=86.6025-.5774x\]
waheguru
  • waheguru
Well I actually had\[x(\tan36+\tan30)=150\tan30\]
Mertsj
  • Mertsj
\[1.3039x=86.6025\]
waheguru
  • waheguru
yea
Mertsj
  • Mertsj
\[x=66.4\]
waheguru
  • waheguru
YOU ARE SO AMAZING
waheguru
  • waheguru
THANK YOU SOOOOOOO MUCH
Mertsj
  • Mertsj
\[e=\frac{66.4}{\tan 30}=115\]
Mertsj
  • Mertsj
So the valley is 115 feet deep.
Mertsj
  • Mertsj
yw
waheguru
  • waheguru
Wow, I thank you guys so much. You really helped me understand
Mertsj
  • Mertsj
Excellent.
waheguru
  • waheguru
its a 100000 metals from me
Mertsj
  • Mertsj
Thanks.

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