A 3,5 m-long stick casts a shadow that measures 5,2 m on the ground what is the height of a flagpole that casts a 29,2 m-long shadow?
since the ratio of height-to-shadow is the same for both objects,
h/29,2 = 3,5/5,2
Now just solve for h.
h/29.2=3.5/5.2
h*5.2=29.2*3.5
5.2h=102.2
5.2h/5.2=102.2/5.2
h=19.65384615
To find the height of the flagpole, we can set up a proportion using the similar triangles formed by the stick and its shadow, and the flagpole and its shadow.
Let's denote the height of the flagpole as 'x'.
The proportion can be set up as follows:
(Length of stick shadow) / (Height of stick) = (Length of flagpole shadow) / (Height of flagpole)
Using the given values, we have:
5.2 m / 3.5 m = 29.2 m / x
Next, we can cross multiply to solve for 'x':
5.2 m * x = 3.5 m * 29.2 m
Simplifying the equation:
5.2x = 102.2
Dividing both sides by 5.2:
x = 102.2 / 5.2
x ≈ 19.65 m
Therefore, the height of the flagpole is approximately 19.65 meters.
To determine the height of the flagpole, we can use the concept of similar triangles.
First, let's establish the relationship between the stick and its shadow. We have a stick that is 3.5 m long and casts a shadow measuring 5.2 m.
Using this information, we can set up a proportion:
Height of stick / Length of shadow of stick = Height of flagpole / Length of shadow of flagpole
Let's plug in the values we know:
3.5 m / 5.2 m = Height of flagpole / 29.2 m
To solve for the height of the flagpole, we cross-multiply and solve for the unknown value:
(3.5 m * 29.2 m) / 5.2 m = Height of flagpole
102.2 m / 5.2 m = Height of flagpole
Height of flagpole = 19.65 m
Therefore, the height of the flagpole is approximately 19.65 meters.