A pole that is
3.2m
tall casts a shadow that is
1.4m
long. At the same time, a nearby tower casts a shadow that is
39.5m
long. How tall is the tower? Round your answer to the nearest meter.
Use this proportion. Cross multiply and solve for x.
3.2/1.4 = x/39.5
To find the height of the tower, we can use the concept of similar triangles. The ratios of corresponding sides of similar triangles are equal.
Let's label the height of the tower as 'h'. We can set up the following proportion:
(height of the pole) / (length of its shadow) = (height of the tower) / (length of its shadow)
We can substitute the given values into the proportion:
3.2m / 1.4m = h / 39.5m
To solve for 'h', we can cross multiply:
1.4m * h = 3.2m * 39.5m
Multiply the numbers on the right side:
1.4h = 126.4
Now, divide by 1.4 to isolate 'h':
h = 126.4 / 1.4
Calculating this, we find that h = 90.2857.
Rounding this to the nearest meter, the height of the tower is approximately 90 meters.