If suzie is standing 50ft away from a bulilding and there is a 100ft latter going from sizie to the top of the buliding. How tall is the building
Pythagorean Theorem:
a^2 + b^2 = c^2
a^2 + 50^2 = 100^2
a^2 + 2,500 = 10,000
a^2 = 7,00
a = 86.6 feet
To determine the height of the building, we can use the concept of similar triangles. In this scenario, imagine that we have two triangles: the smaller triangle formed by Susie, the base of the building, and the point where the ladder touches the building, and the larger triangle formed by Susie, the entire height of the building, and the point where the ladder touches the building.
The two triangles are similar because both have a right angle and share an angle at the top. Since the ratios of corresponding sides of similar triangles are equal, we can set up a proportion using the corresponding sides of the two triangles.
Let's assign variables:
Height of the building = H
Distance of Susie from the base of the building = 50 ft
Distance of Susie from the top of the building = H - 50 ft
Length of the ladder = 100 ft
Using the similar triangles, we can set up the proportion:
(H - 50) / 50 = H / 100
Now we can solve for H, the height of the building. We can cross-multiply and solve the equation:
100(H - 50) = 50H
100H - 5000 = 50H
50H = 5000
H = 5000 / 50
H = 100 ft
Therefore, the height of the building is 100 feet.