David wants to find the height of a building. He places his 44 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 10 feet. How tall is the building? Round your answer to the nearest tenth.
a2+b2=c2
A visual to demonstrate the 44 foot ladder that has its feet resting 10 feet from the house. Please climb this ladder carefully!
(10 points)
The building is
feet tall (rounded to the nearest tenth).
Using the Pythagorean theorem, we can find the height of the building.
Let a be the height of the building and b be the distance from where the ladder rests on the ground to the building.
Using the formula a^2 + b^2 = c^2, where c is the length of the ladder, we have:
a^2 + 10^2 = 44^2
a^2 + 100 = 1936
a^2 = 1836
a ≈ √1836
a ≈ 42.9
Therefore, the building is approximately 42.9 feet tall.
To find the height of the building, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder is acting as the hypotenuse, and the base of the building is one of the sides. Let's call the height of the building "h" and the length of the ladder "c".
We know that the base of the building is 10 feet, and the ladder is 44 feet. Using the Pythagorean theorem, we can set up the equation:
10^2 + h^2 = 44^2
Simplifying the equation:
100 + h^2 = 1936
Subtracting 100 from both sides:
h^2 = 1836
Taking the square root of both sides to isolate "h":
h = √1836
Using a calculator, we find that the square root of 1836 is approximately 42.84. Rounding this to the nearest tenth, we get:
The height of the building is approximately 42.8 feet.
To find the height of the building, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs (a and b) is equal to the square of the length of the hypotenuse (c).
In this case, the ladder represents the hypotenuse, and the distance from the base of the building to the ladder represents one leg. We can label the height of the building as the other leg. Let's call the base of the building b, the height of the building h, and the ladder length c.
According to the problem, we know that b = 10 feet and c = 44 feet.
Using the Pythagorean theorem, we can solve for h:
a^2 + b^2 = c^2
h^2 + 10^2 = 44^2
h^2 + 100 = 1936
h^2 = 1936 - 100
h^2 = 1836
Taking the square root of both sides, we find:
h = √1836
Rounding to the nearest tenth:
h ≈ 42.9 feet
Therefore, the building is approximately 42.9 feet tall.