David wants to find the height of a building. He places his 32 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 17 feet. How tall is the building? Round your answer to the nearest tenth. the building is about?
Using the ladder, the height of the building can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the height of the building and the base of the building).
Let the height of the building be 'h'.
By using the Pythagorean theorem: h^2 + 17^2 = 32^2
Simplifying the equation: h^2 + 289 = 1024
Subtracting 289 from both sides: h^2 = 735
Taking the square root of both sides: h ≈ √735 ≈ 27.1
Therefore, the height of the building is approximately 27.1 feet.
To find the height of the building, we can use the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the length of the ladder) is equal to the sum of the squares of the other two sides.
Let's label the height of the building as 'h' and the distance from the base of the building to the ladder as 'b'. According to the problem, the length of the ladder is 32 feet and the distance to the ladder (base of the building) is 17 feet.
Using the Pythagorean theorem, we have:
h^2 = 32^2 - 17^2
h^2 = 1024 - 289
h^2 = 735
To find the height of the building, we can take the square root of both sides of the equation:
h = √735
Evaluating this expression, we find that the height of the building is approximately 27.07 feet when rounded to the nearest tenth.
To find the height of the building, we can use the concept of similar triangles. In this case, the two triangles we are looking at are the triangle formed by the building, ladder, and the ground, and the smaller triangle formed by the measured base of the building, ladder, and the ground.
We can set up the following proportion:
(height of the building)/(length of the ladder) = (base of the building)/(length of the measured base)
Plugging in the values, we have:
(height of the building)/(32 feet) = (17 feet)/(17 feet)
Simplifying the equation, we have:
(height of the building)/32 = 1
Now, we can solve for the height of the building by multiplying both sides of the equation by 32:
height of the building = 32 feet
Therefore, the height of the building is approximately 32 feet.