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Consider a triangular plot ABC with sides AB = 7m, BC = 5m, and CA = 6m. A vertical lamp -post at the mid point D of AC subtends an angle $30^{\circ}$ at B. The height (in m) of the lamp post is :
Option 1)

$\frac{3}{2}\sqrt{21}$
Option 2)

$\frac{2}{3}\sqrt{21}$
Option 3)

$2\sqrt21$
Option 4)

$7\sqrt{3}$

Answers (1)

best_answer

Trigonometric Ratios of Functions -

$\sin \Theta = \frac{Opp}{Hyp}$

$\cos \Theta = \frac{Base}{Hyp}$

$\tan \Theta = \frac{Opp}{Base}$

- wherein

Trigonometric Ratios of Functions

$\tan 30^{\circ}=\frac{h}{BD}$

$BD=\sqrt 3\: \: h$

So,

$7^{2}+5^{2}=2((\sqrt{3 h})^{2}+3^{2})$

$49+25=2(3h^{2}+9)$

$3h^{2}=28$

$h=\frac{2}{\sqrt 9}\sqrt{21}$

$h=\frac{2}{3}\sqrt{21}$

Option 1)

$\frac{3}{2}\sqrt{21}$

Option 2)

$\frac{2}{3}\sqrt{21}$
Option 3)

$2\sqrt21$

Option 4)

$7\sqrt{3}$

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