1.

The upper `3/4`th portion of a vertical pole subtends an angle `theta`such that tan `theta=3/5`at a point in the horizontal plane through its foot and at a distance 40mfrom the foot. Find the possible height of the vertical pole.

Answer» Let `h` is the height of the vertical pole.
It is given that , `tan theta = 3/5`
We can draw a diagram wuth the given details.
Please refer to video for the diagram.
From the diagram,
`beta = alpha+theta`
`=>tan beta = tan(alpha+theta)`
`=>h/(CD) = (tanalpha+tantheta)/(1-tanalphatantheta)`
`=>h/40 = ((h/4)/40 +3/5)/(1-(h/4)/40(3/5)`
`=>h/40(1-h/160(3/5)) = h/160+3/5`
`=>h/8(800-3h) = 800(h/32+3)`
`=>3h^2-600h+19200 = 0`
`=>h^2-200h+6400 = 0`
`=>(h-40)(h-160) = 0`
`=>h = 40m or h = 160m`


Discussion

No Comment Found

Related InterviewSolutions