# Heights and distance problem

• May 3rd 2011, 03:12 AM
vivek_master146
Heights and distance problem
The angle of elevation from a point(on ground) is 45 degree and after 20 seconds its 30 degree If the aircraft is flying at a constant speed at 360 km/h. Find the height of plane from the ground.

• May 3rd 2011, 04:46 AM
Sambit

angle AOB=45, angle COD=30. AB=CD, CA=DB. A is the initial position of the plane; and C is the position of the plane after 20 seconds. In 20 seconds, the plane covers a distance of 2000 mitres. So AC=2000.

tan(AOB)=tan(45)=1=AB/BO. So AB=BO

tan(COD)=tan(30)=1/sqrt(3)=CD/DO=CD/(DB+BO)=CD/(2000+BO)=AB/(2000+BO)=AB/(2000+AB)

That is AB/(2000+AB) = 1/sqrt(3)

Solving, AB = 2000/{sqrt(3)-1} which is the required height.

EDIT: In case the above link is non-accessible, here is another link http://oi56.tinypic.com/2eldz4n.jpg
• May 3rd 2011, 06:31 AM
Soroban
Hello, vivek_master146!

Quote:

The angle of elevation of a plane from a point on ground is 45 degree
and after 20 seconds it's 30 degrees.
If the plane is flying at a constant speed at 360 km/h, find the altitude of plane .

The answer is 2000√3. . Wrong!

Code:

                  A                   *                 * |               *  |             *    |h           *      |         * 45d    |     O * - - - - - *B             h
http://latex.codecogs.com/png.latex?...,=\,AB \,=\,OB

Code:

                  A    2    C                   . - - - - - *                 . .      *  |               .  .  *      |             .    *h          |h           .  *  .          |         . * 30d  .          |     O * - - - - - * - - - - - *             h _  B    2    D       : - - - √3h - - - - - - :

http://latex.codecogs.com/png.latex?...}A\text{ to }C
. . http://latex.codecogs.com/png.latex?...\!D \:=\:h + 2

http://latex.codecogs.com/png.latex?...\,\sqrt{3}\,h.

http://latex.codecogs.com/png.latex?...{3}-1)h \:=\:2

http://latex.codecogs.com/png.latex?...-1}\text{ km.}