Question

the angle of elevation of a lader leaning against a wall is 60 degree and the foot of the ladder is 4.6m away from the wall. The length of the ladder is???​

Answer 1

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\mathfrak{\orange{\bf{Given}}}}}$

• the angle of elevation of a lader leaning against a wall is 60°
• the foot of the ladder is 4.6m away from the wall

$\Large{\underline{\mathfrak{\orange{\bf{Find}}}}}$

• The length of ladder

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$

Let, by diagram.

• AB be the wall .
• AB be the wall .BC be the ladder .

And,

• <ACB = 60°
• AC = 4.6 m

We Know,

★ Cos θ = Base/Hypotenuse

So,

➥ Cos 60° = AC/BC

➥ Cos 60° = 4.6/BC

[ Cos 60° = 1/2 ]

➥ 1/2 = 4.6/BC

➥ BC = 2 × 4.6

➥ BC = 9.2 m

$\Large{\underline{\underline{\mathfrak{\red{\bf{Hence}}}}}}$

• Height of ladder will be (BC) = 9.2 m

__________________

Answer 2

$\huge\sf\pink{Answer}$

☞ Height of Ladder is 9.2 m

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$\huge\sf\blue{Given}$

✭ Angle of elevation of a ladder leaning against a wall is 60°

✭ Foot of the ladder is 4.6 m away from the wall

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$\huge\sf\gray{To \:Find}$

◈ The length of the ladder?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Let}}$

◕ AB = wall

◕ BC = ladder

◕ ∠ACB = 60°

◕ AC = 4.6 cm

So we know that,

$\underline{\boxed{\sf cos \theta = \dfrac{Adjacent}{Hypothenuse}}}$

Substituting the given values,

➝ $\sf cos \ 60 = \dfrac{AC}{BC}$

➝ $\sf cos \ 60 = \dfrac{4.6}{BC}$

$\sf \bigg\lgroup cos \ 60 = \dfrac{1}{2}\bigg\rgroup$

Substituting the value of cos 60,

➳ $\sf \dfrac{1}{2} = \dfrac{4.6}{BC}$

➳ $\sf BC = 4.6 \times 2$

➳ $\sf \orange{BC = 9.2 \ m}$

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