Trigonometry homework: length of shadow

In summary, the sun was shining on engineer Jack Smith, who was reading in the shadow cast by the pine tree planted by his grandfather Tom Smith. The length of the horizontal part of the shadow was 6.0 m and the height of the vertical part of the shadow on the wall was 3.6 m. The height angle of the rays of the sun was 42degrees. The shadow went along the ground and up the wall, and the height of the pine tree was 5.4m.
  • #1
chawki
506
0

Homework Statement


The sun was shining in the yard of engineer Jack Smith. Jack was reading in the shadow cast by the pine tree planted by his grandfather Tom Smith. The length of the horizontal part of the shadow was 6.0 m and the height of the vertical part of the shadow on the wall was 3.6 m. The height angle of the rays of the sun was 42degrees.

Homework Equations


Find the height of the pine tree.



The Attempt at a Solution


Is it 5.4m!
 
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  • #2
hi chawki! :smile:
chawki said:
The length of the horizontal part of the shadow was 6.0 m and the height of the vertical part of the shadow on the wall was 3.6 m. The height angle of the rays of the sun was 42degrees.

read the question :rolleyes:

the shadow goes along the ground and up the wall :wink:
 
  • #3


Yes, i think I'm right...
we have Tan 42 = h/6
so h= 5.4m
tell me if I'm wrong
 
  • #4
if the height was only 5.4, the shadow would only just reach the wall, and not go up it
 
  • #5


Please i still don't get it...
 
  • #6
have you drawn a diagram?

a diagram is essential for solving questions like this

describe to us what your diagram looks like (including the wall) :smile:
 
  • #7


Here it is
 

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  • #8
hmm … when i said that a diagram is essential, i rather assumed that you would also draw in the right-angled triangle that you're using …

how else does the diagram help? :redface:

(nice tree, btw :smile: … though shouldn't it be taller, for 42° ? :wink:)
 
  • #9


i'm not sure, it is hard :(
i sent you a graph as i found it...
 

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  • #10
ah, now i see what you're doing wrong …

to use tan42°, you need a right-angled triangle, but you've drawn a sort of four-sided triangle :rolleyes:

for the good old three-sided triangle that your professor is expecting you to come up with, you need to draw a horizontal line from the top of that arrow (up the wall) to the tree …

try that! :smile:

(because the little circle you've drawn to show 42° should be at a point, shouldn't it, not a big line? :wink:)
 
  • #11


One word...i'm lost...headache now
 
  • #12
have you drawn that horizontal line?
 
  • #13


WHAT HORIZONTAL LINE...
Can you draw it...and send it to me...i will understand it by my own
 
  • #14
this line …
tiny-tim said:
… you need to draw a horizontal line from the top of that arrow (up the wall) to the tree …

try that! :smile:
 
  • #15


Right...after smoking and drinking big cup of coffee...i found out what you wanted to say..
Tan42 = 3.6/x
so: x=4
and then:
Tan42 =h/(6+4)
h=9m ?
 

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  • #16
yes! :biggrin:

(though i'd just have drawn the smaller triangle, found its height was 5.4, added it to the height of the shadow, and got 9.0 that way :wink:)

ok, now you see the importance of a good diagram, and of being willing to draw extra lines on it? :smile:
 
  • #17


:D all i needed is a cup of coffee LOL
Thank you again :)
 
  • #18
chawki said:
:D all i needed is a cup of coffee LOL

then give up smoking! :wink: o:)
 
  • #19


Thanks guys, I found reading this thread thoroughly entertaining! Big-ups to both of you..
 

What is trigonometry and how is it used to find the length of a shadow?

Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles. It is commonly used to find the length of a shadow by using the properties of similar triangles.

What information is needed to find the length of a shadow using trigonometry?

To find the length of a shadow using trigonometry, you will need to know the angle of elevation of the sun or light source, the height of the object casting the shadow, and the distance between the object and its shadow.

Can trigonometry be used to find the length of a shadow at any time of the day?

Yes, trigonometry can be used to find the length of a shadow at any time of the day as long as you have the necessary information, such as the angle of elevation and the height of the object.

What are the steps involved in using trigonometry to find the length of a shadow?

The first step is to draw a diagram representing the situation. Then, identify the angle of elevation and the height of the object. Next, use the tangent function to find the length of the shadow. Finally, make sure to convert the units to match the given information.

Are there any real-life applications of using trigonometry to find the length of a shadow?

Yes, there are many real-life applications of using trigonometry to find the length of a shadow. For example, architects and engineers use this method to determine the size and placement of shadows for buildings and structures. It is also used in navigation, astronomy, and photography.

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