a 12ft building casts a shadow. The distance from the top of the building to the tip of the shadow is 19ft. Find the length of the shadow.
This forms a right triangle -- so let's use the Pythagorean Theorem.
a^2 + b^2 = c^2
12^2 + b^2 = 19^2
144 + b^2 = 361
b^2 = 217
b = 14.7 ft.
To find the length of the shadow, we can use similar triangles. Similar triangles are triangles that have the same shape, but differ in size.
In this case, we have two similar triangles: one formed by the building, its shadow, and the line from the top of the building to the tip of the shadow, and the other formed by the building, its shadow, and the ground.
Let's assign variables to the unknown lengths. Let the length of the building be 'B', the length of the shadow be 'S', and the distance from the top of the building to the tip of the shadow be 'D'.
In the first triangle, the ratio of the length of the building to the length of the shadow is the same as the ratio of the distance from the top of the building to the tip of the shadow to the length of the shadow:
B / S = D / S
We already know the length of the building (12ft) and the distance from the top of the building to the tip of the shadow (19ft). Plugging these values into the equation, we get:
12ft / S = 19ft / S
Now, we can solve for the length of the shadow by cross-multiplying:
12ft * S = 19ft * S
12ft = 19ft
Simplifying, we get:
S = (12ft * 19ft) / 19ft
The 'ft' units cancel out, leaving us with:
S = 12ft
Therefore, the length of the shadow is 12ft.