Word problem angle of elevation/depression. HELP!

**reiward** · August 11th 2009, 04:42 AM

Please help. I have no idea how to get this.

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.

Please help. Please include an illustration of the problem. Thanks

**Amer** · August 11th 2009, 06:32 AM

Originally Posted by reiward

Please help. I have no idea how to get this.

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.

Please help. Please include an illustration of the problem. Thanks

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)

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

Word problem angle of elevation/depression. HELP!-mod.jpg

Edited: Fix the error

**masters** · August 11th 2009, 06:49 AM

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.

**Amer** · August 11th 2009, 07:15 AM

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

**reiward** · August 11th 2009, 02:55 PM

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)

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

Click image for larger version.

Name: Mod.JPG
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ID: 12457

Edited: Fix the error

thank you so much!

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