# Trigonometry homework: length of shadow

## 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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tiny-tim
Homework Helper
hi chawki!
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 goes along the ground and up the wall

Yes, i think i'm right...
we have Tan 42 = h/6
so h= 5.4m
tell me if i'm wrong

tiny-tim
Homework Helper
if the height was only 5.4, the shadow would only just reach the wall, and not go up it

Please i still don't get it...

tiny-tim
Homework Helper
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)

Here it is

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tiny-tim
Homework Helper
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?

(nice tree, btw … though shouldn't it be taller, for 42° ? )

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

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tiny-tim
Homework Helper
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

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!

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

tiny-tim
Homework Helper
have you drawn that horizontal line?

WHAT HORIZONTAL LINE....
Can you draw it...and send it to me...i will understand it by my own

tiny-tim
Homework Helper
this line …
… you need to draw a horizontal line from the top of that arrow (up the wall) to the tree …

try that!

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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tiny-tim
Homework Helper
yes!

(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 )

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

:D all i needed is a cup of coffee LOL
Thank you again :)

tiny-tim