A point on the ceiling of a room is 12ft. from each of the vertices of a triangle on the floor whose legs are 6ft. A and 8ft. respectively. find the length of the ceiling

length or height?

How many feet is A ?

Length of the ceiling

To find the length of the ceiling, we can use the concept of similar triangles.

Let's label the vertices of the triangle on the floor as A, B, and C. The point on the ceiling is labeled as P.

We have two similar triangles: triangle ABC on the floor and triangle APB on the ceiling.

From the given information, we know that AP = 12 ft, AB = 6 ft, and AC = 8 ft.

In triangle APB, we want to find the length of the ceiling, which is PB.

We can set up a proportion using the corresponding sides of the similar triangles:

AB/AP = BC/PB

Substituting the known values, we get:

6 ft / 12 ft = 8 ft / PB

Now we can solve for PB:

PB = (8 ft * 12 ft) / 6 ft
PB = 16 ft

Therefore, the length of the ceiling, PB, is 16 ft.