I am completely confused when it comes to this problem, I don't even know where to start. I tried just seeing how many times the bridge length goes into the building's shadow but still comes up way short. this is the problem (btw in the real life photo the bridge is 1 cm, and the buildings shadow is 4 cm):
In the aerial photograph below, which was taken when the sun’s elevation was 46.733˚, estimate the height (in meters) of the tallest building in the photo given the length of the bridge over the freeway located near the tip of its shadow is 151.6 meters long.
the shadow is 4 times the length of the bridge
(bldg height) / shadow = tan(sun elev)
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To help you solve this problem, let's break it down step by step:
Step 1: Understand the problem
From the problem statement, we are given the following information:
- The length of the bridge over the freeway near the tip of the building's shadow is 151.6 meters.
- The length of the bridge in the real-life photo is 1 cm.
- The length of the building's shadow in the real-life photo is 4 cm.
- The sun's elevation during the photograph was 46.733˚.
Step 2: Set up the problem
We need to determine the height of the tallest building in meters. To do this, we can use similar triangles. We can set up a proportion between the lengths of the bridge and the building's shadow in the real-life photo.
Step 3: Set up the proportion
Let's assign variables to the unknowns:
- Let x represent the height of the tallest building.
Using the given information, we can set up the proportion as follows:
(Height of the building / Length of the building's shadow) = (Height of the bridge / Length of the bridge)
Or in mathematical terms:
x / 4cm = 151.6m / 1cm
Step 4: Solve the proportion
To solve the proportion, we can cross-multiply and then solve for x:
x * 1cm = 4cm * 151.6m
Simplifying the equation:
x = (4cm * 151.6m) / 1cm
Step 5: Convert the units
To get the height in meters, we need to ensure the units cancel out properly. We can convert centimeters to meters by dividing by 100, as there are 100 centimeters in a meter:
x = (4cm * 151.6) / 1cm / 100
Simplifying the equation further:
x = 606.4/100
x = 6.064 meters
Step 6: Finalize the answer
The height of the tallest building in the photo, given the information provided, is estimated to be approximately 6.064 meters.
Therefore, based on the given details, the height of the tallest building in the aerial photograph is approximately 6.064 meters.