A ladder leaning against a wall make a angle of 60 with the horizontal. If the foot of the ladder is 2.5m away from the wall , find the length of the ladder?

Question

Answer

Problem:

A ladder leaning against a wall make a angle of 60 with the horizontal. If the foot of the ladder is 2.5m away from the wall, find the length of the ladder?

Solution:

Let us consider the following diagram:

Identify Given Information:

The ladder is leaning against a wall

The angle between the ladder and the horizontal is 60 degrees

The distance between the foot of the ladder and the wall is 2.5m

Identify What Needs to be Found:

We need to find the length of the ladder.

Applying Trigonometry:

We can use the trigonometric function of sine to find the length of the ladder. In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

In this case, the opposite side is the height of the ladder on the wall and the hypotenuse is the length of the ladder. So, we can write:

sin(60) = height of ladder on wall / length of ladder

Using the value of sin(60) = √3 / 2, we get:

√3 / 2 = height of ladder on wall / length of ladder

Multiplying both sides by the length of ladder, we get:

length of ladder * √3 / 2 = height of ladder on wall

Now, we need to find the height of the ladder on the wall. From the diagram, we can see that:

height of ladder on wall = distance between foot of ladder and wall * tan(60)

Using the value of tan(60) = √3, we get:

height of ladder on wall = 2.5m * √3

Substituting this value in the previous equation, we get:

length of ladder * √3 / 2 = 2.5m * √3

Dividing both sides by √3 / 2, we get:

length of ladder = (2.5m * √3) / (√3 / 2)

Simplifying this expression, we get:

length of ladder = 5m

Answer:

The length of the ladder is 5 meters.

Answer

Let AB is the height of the wall and AC is the lenght of the wall

BC is the distance between the ladder and the wall i.e 2.5m

Sin 60= BC/AC

Sin 60= 2.5/AC

√3/2=2.5/AC

AC = 5×√3/√3×√3

AC =5√3/3 ans.

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