Question

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°. (see fig. 9.11)

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Answer 1

$\huge\orange{\overbrace{\red{\underbrace{\color{pink}{{ \red\:{Answer}}}}}}}$

Length of the rope is 20 m and angle made by the rope with the ground level is 30°.

Given: AC = 20 m and angle C = 30°

To Find: Height of the pole

Let AB be the vertical pole

In right ΔABC, using sine formula

sin 30° = AB/AC

Using value of sin 30 degrees is ½, we have

1/2 = AB/20

AB = 20/2

AB = 10

Therefore, the height of the pole is 10 m.

Answer 2

$\huge\underbrace\mathcal\green{Question:-}$

α circυs αrτisτ is cℓiмвiทg α 20 м ℓσทg rσρє, ωнicн is τigнτℓy sτrєτcнє∂ αท∂ τiє∂ ƒrσм τнє τσρ σƒ α vєrτicαℓ ρσℓє τσ τнє grσυท∂. iƒ τнє αทgℓє мα∂є вy τнє rσρє ωiτн τнє grσυท∂ ℓєvєℓ is 30°.

$\huge\mathcal\purple{Find:-}$

• нєigнτ σƒ τнє ρσℓє?

$\huge\underbrace\mathcal\blue{Answer:-}$

• ℓєτ AB вє τнє vєrτicαℓ ρσℓє αท∂ AC вє τнє rσρє.

ทσω,

• ∠ACB = 30° and AC = 20m.

• iท Rigнτ αทgℓє∂ τriαทgℓє ABC.

$\boxed{ \sin(30 ) = \frac{perpendicalur}{hypotenuse}}$

➜$\frac{1}{2}=\frac {AB}{AC}$

➜$\frac{1}{2}=\frac{AB}{20}$

вy crσss мυℓτiρℓy, ωє gєτ:-

➜$2AB =20$

➜$AB= \frac{20}{2}$

➜$\boxed{\bold{AB= 10 \: meter}}$

τнєrєƒσrє , τнє нєigнτ σƒ τнє ρσℓє is 10 мєτєr.