A vertical mast is on top of building and is positioned 6 ft from the front edge. The mast casts a shadow perpendicular to the front of the building and the tip of the shadow is 90 ft from the front of the building. At the same time, the 24 ft building casts a 64 ft shadow. What is the height of the mast?
33.75 is the answer
To determine the height of the mast, we can set up a proportion using the similar triangles formed by the mast, its shadow, and the building with its shadow.
Let's denote the height of the mast as 'h' and the length of its shadow as 's'. The height of the building is given as 24 ft, and the length of its shadow is 64 ft.
From the information given, we know that the tip of the shadow of the mast is 90 ft from the front of the building, which means the distance from the front of the building to the base of the mast is 90 ft + 6 ft (the distance from the front edge of the building to the mast) = 96 ft.
Now, let's create a proportion:
(Height of mast / Length of mast shadow) = (Height of building / Length of building shadow)
In terms of the given values, the proportion can be written as:
(h / s) = (24 / 64)
Now we can cross-multiply and solve for 'h':
h * 64 = 24 * s
h = (24 * s) / 64
Since we know the length of the mast shadow is 96 ft (90 ft + 6 ft), we substitute this value into the equation:
h = (24 * 96) / 64
h = 36 ft
Therefore, the height of the mast is 36 ft.