Can someone help me with this word problem.
How far up a wall will an 11m ladder reach, if the foot of the ladder must be 4m from the base of the wall? Round your answer to the nearest tenth.
The ladder will form a right-angled triangle with the wall, so use Pythagoras
x^2 + 4^2 = 11^2
etc
Sure! To solve this word problem, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder represents the hypotenuse, and the distance up the wall represents one of the sides.
Given that the ladder is 11m long and the foot of the ladder is 4m from the base of the wall, you can set up the equation as follows:
(Height of the wall)^2 + 4^2 = 11^2
Simplifying this equation:
(Height of the wall)^2 + 16 = 121
Subtracting 16 from both sides:
(Height of the wall)^2 = 105
To find the height of the wall, take the square root of both sides:
Height of the wall = √105
Using a calculator, the approximate value for √105 is 10.246.
Therefore, the ladder will reach approximately 10.2 meters up the wall.
Sure! To solve this word problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the wall, the ladder, and the ground form a right triangle. The ladder is the hypotenuse, the distance from the base of the wall to the foot of the ladder is one side, and the height we are trying to find is the other side.
Let's call the height we are trying to find "h." According to the Pythagorean theorem, we have:
h^2 + 4^2 = 11^2
Simplifying the equation, we get:
h^2 + 16 = 121
To isolate the height, we subtract 16 from both sides:
h^2 = 121 - 16
h^2 = 105
To find the value of h, we take the square root of both sides:
h ≈ √105
Using a calculator to find the square root of 105, we get:
h ≈ 10.246950767097
Rounding this answer to the nearest tenth, we can conclude that the ladder will reach approximately 10.2 meters up the wall.