A vertical mast is on top of building and is positioned 6' from edge of building. The mast casts a 90' shadow from front of building. Another building 24' tall casts a shadow 64'. What is the height of the mast?
33.75 is the answer
To find the height of the mast, we can use the concept of similar triangles. Let's break down the information given:
1. The mast is positioned 6 feet from the edge of the building.
2. The mast casts a 90-foot shadow from the front of the building.
3. Another building, which is 24 feet tall, casts a 64-foot shadow.
Let's assume the height of the mast is "h" feet.
Now, let's set up a proportion between the similar triangles formed by the two buildings and their shadows:
Height of the mast / Length of the mast's shadow = Height of the other building / Length of the other building's shadow
h / 90 = 24 / 64
To solve for "h," we can cross-multiply and then divide:
h * 64 = 24 * 90
64h = 2160
h = 2160 / 64
h ≈ 33.75
Therefore, the height of the mast is approximately 33.75 feet.
mast casts a 96 foot shadow?
mast height = 24 * (96/64)