Ameter stick casts a shadow 1.4 m long at the same time a flagpole casts a shadow 7.7 m long. The triangle formed by the meterstick and its shadow is similar to the triangle formed by the flagpole and its shadow. How tall is the flagpole?

1.4/1 = 7.7/x

1.4x = 7.7
x = 7.7/1.4
x = 5.5

X over 4 = 30 over 2.5

2.5x= 4•30
----- = 120 divided by 2.5
X = 48 feet

The flagpole is 48 feet tall.

Sam is 4 feet tall and his shadow is 2.5 feet long. If the flagpole has a 30-foot shadow, how tall is the flagpole?

7.7 divided by 1.4 = 5.5m

To find the height of the flagpole, we can use the concept of similar triangles. Similar triangles have proportional sides, meaning the corresponding sides are in the same ratio.

Let's assign variables to the different lengths involved in the problem. Let h be the height of the flagpole, and let x be the length of the shadow cast by the meter stick.

In this case, we have two similar triangles: one formed by the meter stick and its shadow, and the other formed by the flagpole and its shadow.

The length of the meter stick is not given, so we can choose any convenient value. For simplicity, let's assume the meter stick is 1 meter long. Thus, x = 1 meter.

Using the given information that the shadow of the meter stick is 1.4 meters long, we can set up the ratios of the corresponding sides of the triangles:

Height of meter stick / Length of meter stick = Height of shadow of meter stick / Length of shadow of meter stick

1 meter / 1 meter = h / 1.4 meters

Simplifying the equation above, we have:

1 = h / 1.4

To find the value of h, we can cross-multiply:

h = 1 * 1.4 = 1.4 meters

Therefore, the height of the flagpole is 1.4 meters.