Question 1195197: 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.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
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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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  .
The distance of the other point from the mast is  .
The difference of these distances is 20 meters, as it is given in the problem,
so you can write this equation
- = 20,
or
x =  .
Next, tan(30°) =  = 0.57735 and tan(45°) = 1, so
x =  = use your calculator = 27 meters (rounded to the nearest meter). ANSWER
Solved.
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Comment from student : please show me the sketch
My response : I won't even think about doing a sketch for you.
Making sketches is the students' honorable duty and a privilege (!)
Making sketches for a student is not a tutors' job. <<<---=== it would be ANTI-pedagogic from my side to do it . . .
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Hey, what I said above, is the  of a fair student.
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Please confirm by posting a message to me, that you do understand
my writing and agree with this CREDO of a fair student.
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