1. Jul 21, 2011

### MayQueen

1. The problem statement, all variables and given/known data

A tree is leaning 14 degrees from the vertical. The tree casts a 40 foot shadow on the flat ground. The line from the trees shadow to the top of tree creates a 60 degree angle above the horizontal. I need to find the lenght of the tree.

2. Relevant equations

3. The attempt at a solution
I tried everything, i know of but im stuck. I tried using trig but that only gave the lenghts for the outside of the right triangle the tree divides. I need help desperately!!

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Last edited: Jul 21, 2011
2. Jul 21, 2011

### Pi-Bond

The question seems to be missing....you might also want to draw a diagram.

3. Jul 21, 2011

### MayQueen

Ok , Im sorry I didnt realize , that i was the only one with the picture in front of me :) Here you go.

4. Jul 21, 2011

### Pi-Bond

Do you know the sine rule?

5. Jul 21, 2011

### MayQueen

No, can you explain to to me?

6. Jul 21, 2011

### Pi-Bond

7. Jul 21, 2011

### MayQueen

So to use the sine rule i dont need a right triangle?

8. Jul 21, 2011

### Pi-Bond

No, it can be applied to any triangle.

9. Jul 21, 2011

### MayQueen

Im sorry that above question is rather stupid. However based on that explanation from the link, I dont understand this part :

That gives c=2sin(105o)/sin(30o)
which is 4sin(105o).

We can write sin(105o) as sin(150o-45o) then use the sin(A-B) rule to write this as
sin(150o)cos(45o)-cos(150o)sin(45o)
Im confused as to why we can write the above statement. Does it change the answer?

10. Jul 21, 2011

### Pi-Bond

The two answers you get are equivalent, since you applied the identity to sin(105)

4sin(105o)=4( sin(150o)cos(45o)-cos(150o)sin(45o) )

11. Jul 21, 2011

### MayQueen

Ok Great! then according to my calculations the lenght of the tree is 49.8677 ft

12. Jul 29, 2011