Question

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

Answer 1

Answer:

The length of the ladder is : 9.2 m

Given:

➛The angle of elevation of a ladder leaning

against a wall is 60 degrees.

➛The foot of the ladder is 4.6 m away from the

wall.

To Find :

Length of the ladder .

Solution:

We are given,

➛The angle of elevation of a ladder leaning

against a wall is 60 degrees.

➛The foot of the ladder is 4.6 m away from the

wall.

( Refer the Attachment )

Let PQ be the wall .

therefore , PR is the distance of wall from the foot of the ladder.

➛ PR = 4.6 m

➛∠ PRQ is the angle of elevation of ladder

i.e, ∠ PRQ = 60°

We know,

The trigonometric identity ,

${\large{\bold{\green{\boxed{\pink{\star{\rm{ \cos( \theta) = \dfrac{adjacent \: side}{hypotenuse } }}}}}}}}$

${\therefore{\rm{\cos( 60 \degree) = \dfrac{4.6}{l}}}}$

${\bold{\rm{ but \ {\boxed { \cos( 60 \degree) = \dfrac{1}{2}}}}}}$

${\therefore{\rm{\dfrac{1}{2} = \dfrac{4.6}{l}}}}$

${\therefore{\rm{l = 4.6 \times 2}}}$

${\therefore{\bold{\boxed{\rm { l = 9.2 \ m }}}}}$

hence, The length of the ladder is : 9.2 m

Answer 2

$\huge\sf\pink{Answer}$

Length of the Ladder is 9.2 m

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ The Angle of elevation of a ladder

$\rule{110}1$

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

◈ The Length of the Ladder?

$\rule{110}1$

$\huge\sf\purple{Steps}$

$\large\sf\star \: Diagram \: \star$

$\setlength{\unitlength}{1.9cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{C}}\put(10.6,1){\large\sf{B}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(8.6,0.7){\sf{\large{4.6 m}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\qbezier(9.8,1)(9.7,1.25)(10,1.4)\put(9.4,1.2){\sf\large{60^{\circ} }}\end{picture}$

So Now here

◕ AB is the ladder whose Angle of elevation is 60°

◕ BC is the foot of the ladder whose length is 4.6 m

We know that,

$\underline{\boxed{\sf{\red{ cos (\theta) = \dfrac{Base}{Hypotenuse}}}}}$

Here, The Hypotenuse is the Length of the Ladder.

☆ And also we know the the value of $\sf cos(60) = \dfrac{1}{2}$

So on Substituting the given values,

»» $\sf cos (60) = \dfrac{Base}{Hypothenuse}$

»» $\sf \dfrac{1}{2} = \dfrac{4.6}{Hypotenuse}$

»» $\sf Hypotenuse = 2 \times 4.6$

$\qquad \bigg \lgroup \sf \because Cross \ Multiply\bigg\rgroup$

»» $\sf\orange{Hypotenuse = 9.2}$

$\rule{170}3$