Ali is standing 10 meters away from a tree. The distance of his eyes from his feet is 1.5 meter. Given that the distance from his eyes to the top of the tree is 15 meters, find the height of the tree
Answer: see the answer
Explanation
Given:
- The horizontal distance from Ali to the base of the tree = 10 m.
- The vertical distance from Ali’s eyes to his feet = 1.5 m.
- The hypotenuse from Ali’s eyes to the top of the tree = 15 m.
Step-by-step solution:
Let the height of the tree be h. Since Ali’s eyes are 1.5 m above the ground, the height of the tree above Ali’s eyes is h−1.5.
Using the Pythagorean theorem in the triangle formed:
1 0^ 2 + ( h − 1.5 )^ 2 = 1 5 2 Simplify:
100 + ( h − 1.5 )^ 2 = 225 Subtract 100 from both sides:
( h − 1.5 )^ 2 = 125 Take the square root of both sides:
Add 1.5 to both sides to get :
h = 11.18 + 1.5 = 12.68 m
Let the height of the tree be h. Since Ali’s eyes are 1.5 m above the ground, the height of the tree above Ali’s eyes is h−1.5.
Using the Pythagorean theorem in the triangle formed:
Simplify:
Subtract 100 from both sides:
Take the square root of both sides:
Add 1.5 to both sides to get :
This question appeared in
Past Papers (3 times)
CSS MPT Past Papers and Syllabus (1 times)
CSS Past Papers download PDF (1 times)
FPSC 5 Years Past Papers Subject Wise (Solved With Details) (1 times)
This question appeared in
Subjects (1 times)
MATHS MCQS (1 times)
Related MCQs
- There are 8 mango trees in a straight line Distance between each tree is 3 meters. What is the distance between the first tree and the eighth tree?
- Alongside a wall of 225 meters long, 26 trees are planted at equal distance, one tree being at each end of the wall. What is the distance between two consecutive trees?
- The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree is?
- A rectangular lawn 80 meters by 60 meters has two roads each 10 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at Rs. 30 per square meter?
- The height of the Egyptian pyramid is 146.6 meters and a base length is 230.6 meters. Find the volume of that pyramid.
- Mount Everest's height is 29,028 feet. What is it's height in meters?
- I planted ____ tree ? in my garden last year. ____ tree ? has now grown big.
- How many feet are there in 7 meters? If 1 meter = 3.281 feet.
- Tube feet, respiratory tree, and papillae are present in which of the following?
- A tree is 7.5 centimetres high. What will its height in millimetres?
