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Some Application of Trigonomertry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsSome Application of Trigonomertry1 Mark
MCQ
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height $5m$. From a point on the plane the angles of elevation of the bottom and top of the flagstaff are respectively $30^\circ$ and $60^\circ $. The height of the tower is :
  • A
    $5m$
  • ✓
    $2.5m$
  • C
    $2m$
  • D
    $10m$
✓

Answer

Correct option: B.
$2.5m$

Here Height of the tower $= CD = h $ meters, height of the flagstaff $= AD = 5$ meters,
Angle of elevation of top of the tower $=\angle\text{DBC}=30^\circ$ and angle of elevation of the top of the flagstaff from ground $=\angle\text{ABC}=60^\circ$
Now, in triangle $\text{DBC},$
$\tan30^\circ=\frac{\text{h}}{\text{x}}$
$\Rightarrow\frac{1}{\sqrt3}=\frac{\text{h}}{\text{x}}$
$\Rightarrow\text{x}=\text{h}\sqrt3....(\text{i})$
And $\tan60^\circ=\frac{\text{h}+5}{\text{x}}$
$\Rightarrow\sqrt3=\frac{\text{h}+5}{\text{x}}$
$\Rightarrow\sqrt3=\frac{\text{h}+5}{\text{x}}....(\text{ii})$

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