Question

A ladder resting on a vertical wall makes an angle whose tangent is 2.5 with the ground. if the distance between the foot of the ladder and the wall is 50cm. what is the lenght of the ladder?.

Answer 1

Answer:

By using angle of elevation method

Step-by-step explanation:

d=50

theta=2.5

since we need to find the hypotenuse side and adjacent side we use cos theta

hypotenuse =h=were ladder is resting on wall

adj=distance baten foot of ladder to wall

Draw a right angle triangle and mark all these

cos2.5=adj÷hyp

cos 2.5=50÷h

h=50÷cos 2.5

h=50÷1

h=50cm

Hope u understand this

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Answer 2

Answer:

The length of the ladder is $5\sqrt{29}$ cm.

Step-by-step explanation:

Step 1 of 2

Given: A ladder resting on a wall makes an angle whose tangent is 2.5, i.e.,

tanθ = AB/BC

⇒ AB/BC = 2.5

⇒ AB/BC = 25/10

⇒ AB = 25 and BC = 10

Here, AB is the wall and BC is the distance between the foot of the ladder and the wall.

Step 2 of 2

From the figure, AC is the length of the ladder.

To find the length AC.

In ΔABC, by Pythagoras theorem,

$AC^2=AB^2+BC^2$

Substitute the values of AB and BC as follows:

⇒ $AC^2=25^2+10^2$

⇒ $AC^2=625+100$

⇒ $AC^2=725$

⇒ $AC=5\sqrt{29}$

Thus, the length of the ladder is $5\sqrt{29}$ cm.

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