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

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*"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.

*"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

The answer is approximately 84 m.

#### Explanation:

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) =

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

We can thus proceed as,

Then

and

Now further we can write,

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

We get