Question 1202974
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Hi,
Can you help me with the question below:
From a point P due south of a vertical tower, the angle of elevation 
of the top of the tower is 20 degrees . 
From a point Q situated 40 metres from P and due east of the tower, 
the angle of elevation is 35 degrees . Let h metres be the height of the tower.
a. Draw a diagram to represent the situation.
b. Evaluate h correct to the nearest metre
Thank you
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        I will not make a diagram for you,  since I assume that it is your job.

        I will solve the problem,  instead.



<pre>
The distance from the base of the tower to point P horizontally in the southern direction is

    {{{d[south]}}} = {{{h/tan(20^o)}}}.


The distance from the base of the tower to point Q horizontally in the eastward direction is

    {{{d[east]}}} = {{{h/tan(35^o)}}}.


{{{d[south]}}}  and  {{{d[east]}}}  are the legs of a right angled triangle, whose hypotenuse is 40 meters.


So, we write the Pythagorean equation

    {{{(h/tan(20^o))^2}}} + {{{(h/tan(35^o))^2}}} = {{{40^2}}}.    (1)


Substituting the values of tan(20°) = 0.363970  and  tan(35°) = 0.70021  and making all necessary calculations,
I reduce equation (1)  to 


    7.548642*h^2 + 2.03959*h^2 = 1600,


or  9.588234*h^2 = 1600,


which gives   h = {{{sqrt(1600/9.588234)}}} = 12.92 meters.


Rounding to the nearest meter, I get the <U>ANSWER</U>  h = 13 meters.
</pre>

Solved.