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 the answer to the nearest tenth.
To find the height of the building, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder represents the hypotenuse, and the base of the building represents one of the legs. Let's call the height of the building "h".
Using the Pythagorean theorem, we have:
ladder^2 = base^2 + height^2
Plugging in the values, we have:
44^2 = 10^2 + h^2
Simplifying, we get:
1936 = 100 + h^2
Subtracting 100 from both sides, we have:
1836 = h^2
To solve for h, we take the square root of both sides:
√1836 = √h^2
Using a calculator, we find that √1836 ≈ 42.86.
Therefore, the height of the building is approximately 42.86 feet.
Using the Pythagorean Theorem, we can find the height of the building.
Let "h" represent the height of the building.
According to the Pythagorean Theorem, in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the hypotenuse (c) represents the ladder, which is 44 feet.
The base of the building (b), as given in the problem, is 10 feet.
The height of the building (a) is the variable we want to find.
So, using the Pythagorean Theorem, we have:
c^2 = a^2 + b^2
44^2 = a^2 + 10^2
1936 = a^2 + 100
Subtracting 100 from both sides of the equation:
1936 - 100 = a^2
1836 = a^2
Taking the square root of both sides of the equation:
√1836 = √a^2
42.91 = a
Rounding to the nearest tenth, the height of the building is approximately 42.9 feet.
To find the height of the building, we can use the concept of similar triangles. The ratio of the height of the building to the length of the ladder is equal to the ratio of the height of the ladder to the distance between the base of the building and the ladder.
Let's represent the height of the building as "h", the length of the ladder as "l", and the distance between the base of the building and the ladder as "d".
In this case, we have:
h / l = l / d
Substituting the known values, we get:
h / 44 = 44 / 10
Now, we can solve for "h". We cross-multiply and solve the equation:
h = (44 * 44) / 10
Calculating this, we get h = 193.6
Therefore, the height of the building is approximately 193.6 feet.