Question

Consider a triangular plot of abc with sides ab=7m ,bc=5 and ac=6m.Then lamp post at the mid point d of ac subtends 30 degree at b then height of lamp post

Answer 1

We have to consider it as a 3D image.

Answer 2

Answer:

The height of the lamp post is √6 meter

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the problem :

Let AB = 7 m = c

BC = 5 m = a

AC = 6 m = b

Applying cosine formula in ΔABC

$\cos C=\frac{a^2+b^2-c^2}{2ab}\\\\\implies\cos C=\frac{25+36-49}{60}=\frac{8}{15}$

Similarly, using cosine formula in ΔBDC

BD² = BC² + CD² - 2·BC·CD·cos C

Since D is midpoint of AC ⇒ CD = 3 m

⇒ BD² = 25 + 9 - 2 × 5 × 3 × 8/15

⇒ BD = 3√2 m

In ΔBDP,

$\tan\theta=\frac{PD}{BD}\\\\\implies PD=\tan 30\times 3\sqrt{2}\\\\\implies PD=\sqrt 6\text{ meter}$

Therefore, The height of the lamp post is √6 meter