Class 10 Exam > Class 10 Questions > At the foot of a mountain,the elevation of it...
Start Learning for Free
At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain?
Most Upvoted Answer
At the foot of a mountain,the elevation of its summit is 45 degree.Aft...
Community Answer
At the foot of a mountain,the elevation of its summit is 45 degree.Aft...
Given data:
- Elevation of summit = 45 degrees
- After ascending 1000m at 30 degrees inclination, elevation = 60 degrees
Let's solve step by step:
Step 1: Finding the height of the mountain till the 30-degree point
- Let h be the height of the mountain till the 30-degree point
- Tan(30) = h/1000
- h = 1000 * Tan(30)
- h = 1000 * 1/sqrt(3)
- h = 1000/sqrt(3)
Step 2: Finding the height of the mountain till the summit
- Let H be the height of the mountain till the summit
- Tan(45) = (H + h)/x, where x is the distance covered after reaching the 30-degree point till the summit
- We know that Tan(45) = 1
- 1 = (H + 1000/sqrt(3))/x
Step 3: Solving for the height of the mountain
- From the second given condition, Tan(60) = (H + 1000)/x
- sqrt(3) = (H + 1000)/x
- x = (H + 1000)/sqrt(3)
- Substitute x value in the equation from step 2:
- 1 = (H + 1000/sqrt(3))/((H + 1000)/sqrt(3))
- 1 = sqrt(3) * (H + 1000/sqrt(3))/(H + 1000)
- 1 = sqrt(3) * (Hsqrt(3) + 1000)/(Hsqrt(3) + 1000)
- sqrt(3)H + 1000 = Hsqrt(3) + 1000
- H(sqrt(3) - 1) = 0
- H = 0 or sqrt(3) - 1
- Since height cannot be 0, the height of the mountain is:
- H = sqrt(3) - 1 = 1.73 - 1 = 0.73 km = 730 m
Therefore, the height of the mountain is 730 meters.
- Elevation of summit = 45 degrees
- After ascending 1000m at 30 degrees inclination, elevation = 60 degrees
Let's solve step by step:
Step 1: Finding the height of the mountain till the 30-degree point
- Let h be the height of the mountain till the 30-degree point
- Tan(30) = h/1000
- h = 1000 * Tan(30)
- h = 1000 * 1/sqrt(3)
- h = 1000/sqrt(3)
Step 2: Finding the height of the mountain till the summit
- Let H be the height of the mountain till the summit
- Tan(45) = (H + h)/x, where x is the distance covered after reaching the 30-degree point till the summit
- We know that Tan(45) = 1
- 1 = (H + 1000/sqrt(3))/x
Step 3: Solving for the height of the mountain
- From the second given condition, Tan(60) = (H + 1000)/x
- sqrt(3) = (H + 1000)/x
- x = (H + 1000)/sqrt(3)
- Substitute x value in the equation from step 2:
- 1 = (H + 1000/sqrt(3))/((H + 1000)/sqrt(3))
- 1 = sqrt(3) * (H + 1000/sqrt(3))/(H + 1000)
- 1 = sqrt(3) * (Hsqrt(3) + 1000)/(Hsqrt(3) + 1000)
- sqrt(3)H + 1000 = Hsqrt(3) + 1000
- H(sqrt(3) - 1) = 0
- H = 0 or sqrt(3) - 1
- Since height cannot be 0, the height of the mountain is:
- H = sqrt(3) - 1 = 1.73 - 1 = 0.73 km = 730 m
Therefore, the height of the mountain is 730 meters.
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
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain?
Question Description
At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? 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 At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain?.
At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? 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 At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain?.
Solutions for At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? 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 At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? defined & explained in the simplest way possible. Besides giving the explanation of
At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain?, a detailed solution for At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? has been provided alongside types of At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? theory, EduRev gives you an
ample number of questions to practice At the foot of a mountain,the elevation of its summit is 45 degree.After ascending 1000m towards the mountain up,a slope of 30 degree inclination,the elevation is found to be 60 degree.Find the height of the mountain? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup