Class 10 Exam  >  Class 10 Questions  >  A ladder leaning against a wall make a angle ... Start Learning for Free
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?
Most Upvoted Answer
A ladder leaning against a wall make a angle of 60 with the horizontal...
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.
Community Answer
A ladder leaning against a wall make a angle of 60 with the horizontal...
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.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
Explore Courses for Class 10 exam

Top Courses for Class 10

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 Description
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? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 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? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for Class 10. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice Class 10 tests.
Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev