# 'Real word' Trig Question

• Jun 9th 2009, 07:36 AM
prettiestfriend
'Real word' Trig Question
ONE
The angle of depression from the top of a 25-m high building to the top of the building across the street is 5 degrees and to the floor of the building is 47 degrees. What is the heigh of the other building and how wide is the tstreet.

State answers to the nearest meter

TWO
A flag pole is tied to the ground by two steel cables. One cable is 27 metres long and the other is 19 meters. The cables are attached to the ground at points A and B that are 5 meters from each other. The points A and B and the foot of the flagpole are in a straight line. What is the height of the flagpole, if the cables attached to it 1.5 below its top. STate your answers to the nearest tenth of a meter.

I LITERALLY have no idea how to do these.
• Jun 9th 2009, 07:48 AM
Quote:

Originally Posted by prettiestfriend
ONE
The angle of depression from the top of a 25-m high building to the top of the building across the street is 5 degrees and to the floor of the building is 47 degrees. What is the heigh of the other building and how wide is the tstreet.

State answers to the nearest meter

.

First of all , draw a diagram and you will get 2 triangles .

Let the width of the street be y .

tan 47 =25/y . You can find the width .

tan 5= h /y(the answer above)

Final height = 25-h
• Jun 9th 2009, 10:13 AM
aidan
Quote:

Originally Posted by prettiestfriend

...

TWO
A flag pole is tied to the ground by two steel cables. One cable is 27 metres long and the other is 19 meters. The cables are attached to the ground at points A and B that are 5 meters from each other. The points A and B and the foot of the flagpole are in a straight line. What is the height of the flagpole, if the cables attached to it 1.5 below its top. STate your answers to the nearest tenth of a meter.

I LITERALLY have no idea how to do these.

Quote:

First of all , draw a diagram and you will get 2 triangles.

Label the distance from the shorter cable where it attached to the ground (at point B) to the base of the flag pole as 'b'

Label the distance from the base of the flag pole to the longer cable where it is attached to the ground (at Point A) as 'b+5'

Label the distance from the base of the flag pole to the POINT WHERE THE CABLES ARE ATTACHED near the top of the flag pole as 'h'

You should recognize (from your sketch) that you have two right triangles.

Equation1
$27^2 = h^2 + (b+5)^2$
&
Equation2
$19^2 = h^2 + b^2$

subtracting

$27^2 - 19^2 = (b+5)^2 - b^2$

expanding the () part

$27^2 - 19^2 = b^2 + 10b + 5^2 - b^2$
some simplification
$27^2 - 19^2 = 10b + 25$
&more
$27^2 - 19^2 - 25 = 10b$
& dividing
$\frac{27^2 - 19^2 - 25}{10} = b$

Plug that back into Equation2 to get the dimension 'h' and then ADD the 1.5 metres to the top of the flag pole.

$h = \sqrt{19^2 - b^2 }$

& finally the HEIGHT of the flagpole is $h + 1.5$