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  • From a point P on the ground, the angle of elevation of the top of a tower is 30o and that of the top of the flag-staff fixed on the top of the tower is 45o. If the length of the flag-staff is 5 m, find the height of the tower. (U

From a point P on the ground, the angle of elevation of the top of a tower is 30o and that of the top of the flag-staff fixed on the top of the tower is 45o. If the length of the flag-staff is 5 m, find the height of the tower. (Use \sqrt{3}=1.732)

 

 

Answers (1)

Let AB denote the height of the tower and BC denote the height of the flag.

        \mathrm{\tan 30\degree = \frac{AB}{AP}}

        \mathrm{AP = \sqrt3 AB \qquad -(i)}

        \mathrm{\tan 60\degree = \frac{AC}{AP}}

        \mathrm{AP = \frac{1}{\sqrt3}(AB + 5)\qquad -(ii)}

    From (i) and (ii)

        \mathrm{\frac{1}{\sqrt3}(AB + 5)= \sqrt3AB}

        \mathrm{AB + 5 = 3AB}

        \mathrm{2AB = 5}

        \mathrm{AB = 2.5}

Height of the tower is 2.5 m

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