SOLUTION: 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

Question 1202974: 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

Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
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
~~~~~~~~~~~~~~~~~~~

        I will not make a diagram for you, since I assume that it is your job.
        I will solve the problem, instead.

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

     = .


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

     = .


  and    are the legs of a right angled triangle, whose hypotenuse is 40 meters.


So, we write the Pythagorean equation

     +  = .    (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 =  = 12.92 meters.


Rounding to the nearest meter, I get the ANSWER  h = 13 meters.

Solved.

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