The angle of elevation of the top point P of the vertical tower PQ of height ‘h’ from a point A is 45° and from a point B, the angle of elevation is 60°, where B is a point at a distance ‘d’ from the point A measured along the lines AB which makes an angle 30° with AQ. Prove that d =h(3^1/2 -1)

ananya bhat Grade: 11

        The angle of elevation of the top point P of the vertical tower PQ of height ‘h’ from a point A is 45° and from a point B, the angle of elevation is 60°, where B is a point at a distance ‘d’ from the point A measured along the lines AB which makes an angle 30° with AQ. Prove that d =h(3^1/2 -1)

8 months ago

Answers : (2)

Susmita

425 Points

							I cannot attach an image.But follow the steps one by one.
Draw a triangle APQ.angle PQA=90.PQ=h.angle PAQ=45.Say AQ=l.
h/l=tan45
Or,l=h
Now draw a point inside the triangle.This point is B.join AB.AB=d.Drop a perpendicular from B on AQ.name the touching point M.This will from another triangle ABM.angle BAM=30.say AM=x and BM=y.say BN=x'.
SO l=x'+x
Or,h=x'+x
We can find out x from triamgle ABM.
cos30=x/d
Or,x=root(3)d/2
Sin30=y/d
Or,y=d/2
Join PB.drop a perpendicular from B on PQ.name the touching point N.angle PBN=60.NQ=y.PN=h-y.
tan60=(h-y)/x'
x'=(h-d/2)/root3
Put these values in l=h=x+x' and you will get answer.

8 months ago

Susmita

425 Points

							Typing here is really painful.I typed at one place,it appeared at another place.
After "BM=y" please do the drawing "join PB".then go back to BN=x' and  do each step.

8 months ago

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