Question

the height of conical tent is 9m. a vertical pole of 6m height is placed 4m away from its centre such that it touches the surface. Find the Slant height of the tent from the base to a point where pole touches it

Answer 1

The slant height of the tent from the base to the point where pole touches it will be 10 m.

Step-by-step explanation:

See the attached diagram.

Here, CD = 9 m, EF = height of pole = 6 m.

Now, we have to find BF (x), if DE = 4 m and we assume that BE = y.

Now, Δ BCD and Δ BFE are similar triangles.

{Since DC ║ EF and DB and CB are the transverse lines}

So, we can write $\frac{BD}{BE} = \frac{DC}{EF}$

⇒ $\frac{y + 4}{y} = \frac{9}{6}$

⇒ y = 8 m.

Now, BF² = BE² + EF² {Applying Pythagoras Theorem }

⇒ x² = y² + 6²

⇒ x² = 8² + 6² = 100

⇒ x = 10 m

Therefore, the slant height of the tent from the base to the point where pole touches it will be 10 m. (Answer)