The length of a shadow of a building is 27 meters. The distance from the top of the building to the tip of the shadow is 38 meters. what is the height of the building?
h^2+27^2 = 38^2
To find the height of the building, we can use similar triangles. The length of the shadow is the base of one triangle, and the height of the building is the corresponding side. The distance from the top of the building to the tip of the shadow is the diagonal of the larger triangle, and it corresponds to the hypotenuse.
Let's define our variables:
Let "x" be the height of the building.
We know that the length of the shadow (base of the smaller triangle) is 27 meters, and the distance from the top of the building to the tip of the shadow (hypotenuse of the larger triangle) is 38 meters.
Using the properties of similar triangles, we can set up the following proportion:
x/27 = 38/x
To solve this equation, we can cross-multiply:
x * x = 27 * 38
x^2 = 1026
Taking the square root of both sides gives us:
x = √1026
Now we can calculate the height of the building (x) using a calculator or approximation tools.