A tree broke from a point but did not separate. If the point from where it broke is 7 m above the ground and its top touches the ground at the distance of 24 m from its foot, find out the total hieght of the tree before it broke.
Math chap 9 ex 9:4 Ouestion 11
Use the pythagorean theorem:
sum of squares of two sides of a right triangle = square of hypotenuse.
7^2 + 24^2 = hypotenuse^2
Add hypotenuse value to 7 for total height.
I hope this helps.
To find the total height of the tree before it broke, we can use the Pythagorean theorem. Let's represent the total height of the tree as 'h'.
According to the problem, the top of the tree touches the ground at a distance of 24 m from its foot. This forms a right triangle where the height of the tree is the vertical leg and the distance from the foot to the point where it broke is the horizontal leg.
Using the Pythagorean theorem, we have:
h^2 = (24^2) + (7^2)
h^2 = 576 + 49
h^2 = 625
Taking the square root of both sides, we get:
h = √625
h = 25 meters
Therefore, the total height of the tree before it broke was 25 meters.
To find the total height of the tree before it broke, we can use basic trigonometry.
Let's assume the total height of the tree before it broke is represented by the variable h.
According to the problem, the tree broke from a point but did not separate, meaning that both the top part and the bottom part are still connected. This forms a right triangle, where the height of the tree (h) is the hypotenuse, the distance from the foot of the tree to the point where it broke is the base, and the distance from the point where it broke to the top touching the ground is the perpendicular height.
We are given that the base (distance from the foot to the point where it broke) is 24 m, and the perpendicular height (distance from the point where it broke to the top touching the ground) is 7 m.
Using Pythagoras' theorem, we can write the equation:
h^2 = base^2 + perpendicular height^2
h^2 = 24^2 + 7^2
h^2 = 576 + 49
h^2 = 625
Taking the square root of both sides to solve for h, we get:
h = √625
h = 25
Therefore, the total height of the tree before it broke is 25 meters.