Question 1195197
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The angle of elevation of the top of a mast from a point A is 30°. 
When the observer moves 20 metres towards the foot of the mast, 
the angle of elevation becomes 45°.
Calculate, to the nearest metre, the height of the mast.
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<pre>
Make a sketch.


Let x be the height of the mast, in meters.


In the sketch, find two righ-angled triangles with the right angle
at the base of the mast.


The distance of the point A from the mast is  {{{x/tan(30^o)}}}.

The distance of the other point from the mast is  {{{x/tan(45^o)}}}.


The difference of these distances is 20 meters, as it is given in the problem, 
so you can write this equation

    {{{x/tan(30^o)}}} - {{{x/tan(45^o)}}} = 20,

or

    x = {{{20/(1/tan(30^o)-1/tan(45^o))}}}.


Next, tan(30°) = {{{sqrt(3)/3}}} = 0.57735  and tan(45°) = 1,  so

    x = {{{20/(1/0.57735-1/1)}}} = use your calculator = 27 meters (rounded to the nearest meter).    <U>ANSWER</U>
</pre>

Solved.


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<U>Comment from student</U> : please show me the sketch



<U>My response</U> : I won't even think about doing a sketch for you.



<H3>Making sketches is the students' honorable duty and a privilege (!)</H3>


Making sketches for a student is not a tutors' job.    &nbsp;&nbsp;&nbsp;&nbsp;<<<---=== &nbsp;&nbsp;&nbsp;&nbsp;it would be &nbsp;ANTI-pedagogic from my side to do it . . . 



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Hey, &nbsp;what I said above, &nbsp;is the &nbsp;{{{highlight(highlight(highlight(CREDO)))}}} &nbsp;of a fair student.



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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Please confirm by posting a message to me, that you do understand 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;my writing and agree with this CREDO of a fair student.


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