Math Is Fun Forum

demha

Member

Registered: 2012-11-25

Posts: 195

Trigonometry

I need a little help.

here is the question:
You have collected data on several buildings.  For each building, you are given the angle of the line of sight up to the top of the building, and the distance to the building.  Calculate the height of each building.
 

15. Building 1 Angle 71o Distance 20 meters

Now I know I can set it up either way:

tan71 = h/20

OR

h = 20tan71

I just don't have an idea as to how to solve it. I would really appreciate step by step help. There are more questions similar to this but, I want to know how to do this one so I can try to do the others.

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Trigonometry

After doing some research I figured it out!

15. Building 1 Angle 71o Distance 20 meters - i said F
A 89.26 m
B 74.23 m
C 25.62 m
D 19.23 m
E 67.23 m
F 58.08 m

16. Building 2 Angle 45o Distance 10 meters - i said D
A 4.13 m
B 8.73 m
C 25.62 m
D 10.00 m
E 5.46 m
F 58.08 m

17. Building 3 Angle 20o Distance 15 meters - i said E

A 4.13 m
B 8.73 m
C 25.62 m
D 10.00 m
E 5.46 m
F 58.08 m

18. Building 4 Angle 5o Distance 47.22 meters - i said A
A 4.13 m
B 8.73 m
C 25.62 m
D 10.00 m
E 5.46 m
F 58.08 m

19. Building 5 Angle 1o Distance 500 meters - I said B
A 4.13 m
B 8.73 m
C 25.62 m
D 10.00 m
E 5.46 m
F 58.08 m

~~~
For number 20, I am having a little trouble finding out how to figure this problem out. I could definitely use help on this.

20. You have climbed to the top of a tall tree. When you get to the top, you use your clinometer to discover that the angle between the tree and the line of sight to your red lunchbox is 30o. You know you left the lunchbox 20 meters from the base of the tree. How tall is the tree? (Careful! This is a little different than the building problems!)

A 75.36 m
B92.09 m
C20.17 m
D51.25 m
E 18.95 m
F 34.64 m

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

SteveB

Member

Registered: 2013-03-07

Posts: 595

Re: Trigonometry

20. You have climbed to the top of a tall tree. When you get to the top, you use your clinometer to discover that the angle between the tree and the line of sight to your red lunchbox is 30o. You know you left the lunchbox 20 meters from the base of the tree. How tall is the tree? (Careful! This is a little different than the building problems!)

A 75.36 m
B 92.09 m
C 20.17 m
D 51.25 m
E 18.95 m
F 34.64 m

I am not sure whether the angle 30 is perhaps supposed to be the angle made with the vertical line of the tree and the line towards
the ground to the lunchbox . If this understanding is correct then you could work out the other angle using the fact that the
3 angles of a triangle add up to 180 meaning that if one is 90 then first do 180-90 to get the sum of the other two then
30 + 60 = 90
On this basis perhaps it is trying to lead to 20*Tan(60).

Notice you can get the same result by using h as the adjacent (with TAN) and 20 as opposite.
Tan (30) = opposite/adjacent
Tan (30) = 20 / h
h = 20 / (Tan(30)) = ...

Or with 60 degrees make sure that the "opposite" is indeed opposite the angle and do it that way.

It did wonder whether the hypotenuse was going to be 20 (direct line, rather than horizontal), but it does say the base of the
tree, and this would not fit any of the options anyway so that cannot be the case.
It might be a good idea to draw a diagram getting the measurements according to an approximate scale if you are not sure.
My first answer is one of the options, and I suppose if it is a tall tree the angle of 60 degrees from horizontal would be more likely.

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Trigonometry

I have an idea of how to do it. Not sure if it is exactly correct:

20/x = tan[30]

This gives me the answer of 36.64 which is answer F in #20.

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry

Hi demha;

F is correct.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SteveB

Member

Registered: 2013-03-07

Posts: 595

Re: Trigonometry

You have probably worked this out anyway by now but:

Please note that:

20*Tan(60) = 20 / (Tan(30)) = 36.64 (to 2 dp.) [Answer F]

I was trying to say that those two were the same: If you swap round the "opposite" and "adjacent" then you are using
the other (non right) angle. That is to say when you have three angles in a triangle where one is 90 the other two must
equal 90. So if you are given the angle that you would not have usually used you can either set up the opposite and
adjacent carefully (you have to do so anyway in fact) or calculate the other angle and do it the way you were.

(Also notice that Tan(A) * Tan(90-A) = 1 by the way - a thing I found out from another thread.)

I don't think any of the other possible choices were really going to be likely. 11.55 wasn't one of them for instance.
I suppose I didn't want to write that it was 'F' when I wrote the post because it would make things too easy.