# Word problem angle of elevation/depression. HELP!

• Aug 11th 2009, 05:42 AM
reiward
Word problem angle of elevation/depression. HELP!

From the top of the building, the angle of elevation of the top of a 120 ft tower is 10 degrees. From a window 6ft below the top of the building, the angle of depression of the base of the tower is 30 degrees. Determine the height of the building and the distance between the tower and the building.

• Aug 11th 2009, 07:32 AM
Amer
Quote:

Originally Posted by reiward

From the top of the building, the angle of elevation of the top of a 120 ft tower is 10 degrees. From a window 6ft below the top of the building, the angle of depression of the base of the tower is 30 degrees. Determine the height of the building and the distance between the tower and the building.

in the picture I attached

$Y+X+6=120$....(1)

$\tan 10^0=\frac{X}{D}$....(2)

$\tan 30^0=\frac{Y}{D}$.....(3)

find X ,Y with respect to D
From (2)
$D\tan 10^0 = X$

From (3)
$D\tan 30^0= Y$

sub X,Y values in (1)

$D\tan 10^0+D\tan 30^0+6 =120$

Attachment 12457

Edited: Fix the error
• Aug 11th 2009, 07:49 AM
masters
Quote:

Originally Posted by Amer
in the picture that I attached you can see that

$x+120=6+y=\text{the building height}$

$\tan 10^0 = \frac{x}{D}$ .....(1)

$\tan 30^0 = \frac{y}{D}$.......(2)

find D value with respect to x,y
from (1)

$x=D\tan 10^0$

from (2)
$y=D\tan 30^0$ sub D values in $x+120=6+y$

$D\tan 30^0 + 120 = D\tan 10^0 + 6$ equation with one variable you can find it
Attachment 12456

Amer,

I read it as though the tower was taller than the building and the angle of elevation from the top of the building to the top of the tower is 10 degrees. Your figure shows the angle of depression to the top of the tower is 10 degrees.
• Aug 11th 2009, 08:15 AM
Amer
Quote:

Originally Posted by masters
Amer,

I read it as though the tower was taller than the building and the angle of elevation from the top of the building to the top of the tower is 10 degrees. Your figure shows the angle of depression to the top of the tower is 10 degrees.

Thanks Master

I forgot to see the meaning of elevation in the dictionary sorry I fixed the error
• Aug 11th 2009, 03:55 PM
reiward
Quote:

Originally Posted by Amer
in the picture I attached

$Y+X+6=120$....(1)

$\tan 10^0=\frac{X}{D}$....(2)

$\tan 30^0=\frac{Y}{D}$.....(3)

find X ,Y with respect to D
From (2)
$D\tan 10^0 = X$

From (3)
$D\tan 30^0= Y$

sub X,Y values in (1)

$D\tan 10^0+D\tan 30^0+6 =120$

Attachment 12457

Edited: Fix the error

thank you so much! :)