A pole that is 2.9m tall casts a shadow that is 1.39m long. At the same time, a nearby building casts a shadow that is 36.75m long. How tall is the building.
To find the height of the nearby building, we can use the concept of similar triangles.
Let's denote the height of the building as 'h_B' and the length of its shadow as 's_B.' Then, we can set up the following proportion:
(height of the pole) / (length of the pole's shadow) = (height of the building) / (length of the building's shadow)
Substituting the values given in the problem, we have:
2.9m / 1.39m = h_B / 36.75m
Now, let's solve for 'h_B' by cross-multiplying:
(2.9m)(36.75m) = 1.39m(h_B)
h_B = (2.9m)(36.75m) / 1.39m
h_B = 77.25m
Therefore, the nearby building is approximately 77.25 meters tall.
2.9 / 1.39 = x / 36.75
Cross multiply:
1.39x = 2.9 * 36.75
1.39x = 106.575
x = 76.673 m