really stuck

[iain]

In order to find the height of a inaccessible tower , a theodolite was set up at point A, due south of the tower , where the angle of elevation was measured at 27.32 degrees. The theodolite was moved to point B, 210 Metre's due east of A, where the angle of elevation was measured at 26 degrees.
Assuming that readings were taken at at the same height above sea level


What height is the mast ?

 

[mmm4444bot]

What have you thought about or tried, thus far?

We would appreciate knowing where you are stuck, in this exercise.

 

[iain]

all of it .. If C was the bottom of mast at 90 deg to theodolite. If D was top of mast ...Then Triangle ACD ...AC=CD/tan27.6 Triangle BCD .. BC=CD/Tan26
Using Pythag Theory and replacing values .. BCsquare= 200square +AC square so ....

CD/Tan 26 Square = 210 square + CD/tan27.6 square getting a bit lost after that ...

which gives 2.05 *cd square = 210 square + 1.91 * CD square

...(4.598 * cd) sqr= 210 sqr + (3.64 * CD)sqr

...CD= ?
cant finish it

 

[DrPhil]

In order to find the height of a inaccessible tower , a theodolite was set up at point A, due south of the tower , where the angle of elevation was measured at 27.32 degrees. The theodolite was moved to point B, 210 Metre's due east of A, where the angle of elevation was measured at 26 degrees.
Assuming that readings were taken at at the same height above sea level

If C was the bottom of mast at 90 deg to theodolite. If D was top of mast ...Then Triangle ACD ...AC=CD/tan27.6 Triangle BCD .. BC=CD/Tan26
Using Pythag Theory and replacing values .. BCsquare= 200square +AC square so ....

CD/Tan 26 Square = 210 square + CD/tan27.6 square getting a bit lost after that ...

which gives 2.05 *cd square = 210 square + 1.91 * CD square

...(4.598 * cd) sqr= 210 sqr + (3.64 * CD)sqr

...CD= ?
cant finish it

The problem gave you TOO MUCH information. Since you don't know the distance of A from the mast, you can't convert the tangent of the angle into a distance.

Concentrate on point B (and triangle BCD), for which you know both the angle of elevation (26°) AND the distance BC=210m.