Stephanie casts a shadow of 1.2m and she is 1.8m tall. A wind turbine casts a shadow of 10m at the same time that Stephanie measured her shadow. Draw a diagram of this situation and then calculate how tall the wind turbine is.
Use a proportion to solve this problem.
1.2 / 1.8 = 10/x
Cross multiply and solve for x.
What about the diagram?
To calculate the height of the wind turbine, we can set up a proportion using the lengths of the shadows and the heights.
Let's draw a diagram to visualize the situation:
Stephanie (1.8m) ---[1.2m Shadow]---X (Turbine)---[10m Shadow]
Now, let's set up the proportion:
height of Stephanie / length of Stephanie's shadow = height of the wind turbine / length of the turbine's shadow
Using the given values, we can write the equation:
1.8m / 1.2m = h / 10m
To solve for h (height of the wind turbine), we can cross multiply:
1.8m × 10m = 1.2m × h
18m² = 1.2m × h
Dividing both sides by 1.2m:
18m² / 1.2m = h
15m = h
Therefore, the height of the wind turbine is 15 meters.