Question

7. A ladder learning against a wall makes an angle of 60° with the horizontal.
If the foot of the ladder is 2.5m away from the wall, the length of the ladder is​

Answer 1

Answer:-

According to the Question

It is given that ladder learning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5m away from the wall.

we have to calculate the length of the ladder .

we use here the concept of application of trigonometry.

• ∅ = 60°
• Distance between wall & ladder , b = 2.5

Using formula for calculating the length of ladder .

• Cos∅ = B/H

where,

• ∅ denote Angle
• B denote distance between wall & ladder
• H denote length of ladder

Substitute the value we get

$\longrightarrow$ Cos60° = 2.5/H

$\longrightarrow$ 1/2 = 2.5/H

$\longrightarrow$ H = 2.5×2

$\longrightarrow$ H = 5cm

• Hence, the length of the ladder is 5 cm.

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Answer 2

Answer:

Given :-

• A ladder learning against a wall makes an angle of 60° with the horizontal.
• The foot of the ladder is 2.5 m away from the wall.

To Find :-

• What is the length of the ladder.

Formula Used :-

$\mapsto \sf\boxed{\bold{\pink{cos\theta =\: \dfrac{Base}{Hypotenuse}}}}$

Solution :-

Let,

$\mapsto$ Length of ladder = L cm

Given :

$\bigstar \: \: \rm{\bold{Base =\: 2.5\: m}}$

$\bigstar\: \: \rm{\bold{\theta =\: 60^{\circ}}}$

According to the question by using the formula we get,

$\longrightarrow \sf cos60^{\circ} =\: \dfrac{2.5}{L}$

As we know that, [ cos60° = 1/2 ]

$\longrightarrow \sf \dfrac{1}{2} =\: \dfrac{\dfrac{25}{10}}{L}$

$\longrightarrow \sf \dfrac{1}{2} =\: \dfrac{25}{10} \times \dfrac{1}{L}$

$\longrightarrow \sf \dfrac{1}{2} =\: \dfrac{25}{10L}$

By doing cross multiplication we get,

$\longrightarrow \sf 10L =\: 25(2)$

$\longrightarrow \sf 10L =\: 50$

$\longrightarrow \sf L =\: \dfrac{5\cancel{0}}{1\cancel{0}}$

$\longrightarrow \sf L =\: \dfrac{5}{1}$

$\longrightarrow \sf\bold{\red{L =\: 5\: cm}}$

$\therefore$ The length of the ladder is 5 cm .