What is the height of the tower to the nearest metre?

"David walks along a straight road. At one point he notices a tower on a bearing of 053 with an angle of elevation of 21 degrees. After walking 230 m, the tower is on a bearing of 342, with an angle of elevation of 26 degrees. Find the height of the tower correct to the nearest metre."

I would prefer if you were able to provide a diagram of the problem. I cannot seem to visualise it on the 3D plane. The answer is 84 metres for those who were wondering.

1 Answer
Jul 4, 2018

The answer is approximately 84 m.



Refereeing to the above diagram,
Which is a basic diagram, so hope you can understand,

We can proceed the problem as follows:-

T= Tower
A= Point where the first observation is made
B= Point where second observation is made

AB= 230 m (given)

Dist. A to T =d1
Dist B to T = d2
Height of the tower= 'h' m

C and D are points due north of A and B.
D also lies on the ray from A through T.

h (height of the tower) =
# d1 tan(21°) = d2 tan(26°) #----- (a)

as the distances are very short, AC is parallel to BD

We can thus proceed as,

#angle CAD=53° = angle BDA# (alternate angles)

#angle DBT=360-342=18°#

Then #angle BTD=180-53-18=109° #

and #angle BTA=71°#

Now further we can write,

#230^2 = d1^2 +d2^2 -2d1.d2cos(71°)#

Now on putting the value of d1 and d2 from eqn. (a)

We get #d1# as #218.6 m#

#h=d1 tan(21°)=83.915m# which is approx. 84 m.