Question

Height of a pole is 8 find the length of rope tied with it is top from a point on the ground at a distance of 6 metre from the bottom

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Length\:of\:rope=10\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Height \: of \: pole(AB) = 8 \: m \\ \\ \tt: \implies Distance \: between \: leg \: of \: pole \: and \: end \:point \: of \: rope(BC) = 8 \: m \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length \: of \: rope(AC) = ?$

• According to given question :

$\bold{Using \: phythgoras \: theorem} \\ \tt: \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ \tt: \implies {(AC)}^{2} = {(AB)}^{2} + {(BC)}^{2} \\ \\ \tt: \implies {AC}^{2} = {8}^{2} + {6}^{2} \\ \\ \tt: \implies {AC}^{2} = 64 + 36 \\ \\ \tt: \implies {AC}^{2} =100 \\ \\ \tt: \implies {AC}^{2} = {10}^{2} \\ \\ \tt: \implies AC = \sqrt{ {10}^{2} } \\ \\ \tt: \implies AC = \sqrt{10 \times 10} \\ \\ \tt: \implies AC= \sqrt{2 \times 5 \times 2 \times 5} \\ \\ \tt: \implies AC= \sqrt{2 \times 2 \times 5 \times 5} \\ \\ \tt: \implies AC = 2 \times 5 \\ \\ \green{\tt: \implies AC= 10 \: m} \\ \\ \green{\tt{ \therefore length \: of \: rope \: is \: \: 10 \: m}}$

Answer 2

Answer:

Length of rope = 10 m

Step-by-step explanation:

Given,

Height of pole = 8 m

Distance of point from bottom of pole = 6 m

We know that, pole is perpendicular to the ground.

So when rope is tied fron the top os the pole to the point on ground, it forms an right triangle.

In this triangle,

Perpendicular ( p) = 8 m (height of pole)

Base (b) = 6 cm (distance between the point and bottom of pole)

Hypotenuse (h) = length of rope

By Pythagoras theorem,

(hypotenuse)^2 = (perpendicular)^2 + (base)^2

By applying values we get,

h^2 = p^2 + b^2

h^2 = (8)^2 + (6)^2

h^2 = 64 + 36

h^2 = 100

h = √100 = 10 m

Hence,length of rope tied from top of pole to the point = 10 m