Transition Math Project: Summer Institute 2005
Problem/Task Set
Diablo Canyon Dam
Task:
Diablo Canyon Dam experienced heavy flooding in October 2003. The top of the dam was
destroyed. The engineers need to calculate how much height was lost. The original dimensions
were as follows: the height was 170 feet, the distance across the canyon was 100 feet, and the
thickness of the dam was 15 feet.
A surveyor from Seattle City Light was able to get the following measurements. Although she
could not get to the base of the dam, she got as close as possible. She measured the angle of
elevation to the current ruined top of the dam as 35.500. She moved 135 feet farther back from
the dam along a level road. The new angle of elevation was 21.170.
Write a response to the engineers, stating the amount of height lost as a result of the flood.
Explain your solution using detailed calculations, diagrams and verbal explanations.
Teacher Notes
Standards addressed:
2.2 uses diagrams and words to clearly communicate mathematical ideas.
2.3 produce mathematically valid symbolic arguments to support a conclusion.
5.4 recognize and apply the basic right triangle trigonometric relationships to
solve problems
Scaffolding:
There is extraneous information. Keep the focus to a two-dimensional picture. If students are
struggling with the shape of the dam, tell them to assume that the cross-section is rectangular.
Before giving the problem have students measure an angle of elevation with a protractor, string
and a penny. The problem could then be changed to finding the height of the school stadium or a
building on the grounds. A model of the protractor, string and penny is as follows:
Sample Solution:
(see next page)
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Transition Math Project: Summer Institute 2005
Problem/Task Set
Extension Questions: After finding out how to measure volume, the problem could be brought
back o find the volume of water behind he dam. OR
You could have the students find the volume of the missing concrete. Ask what that amount of
concrete would fill (in terms of their classroom).
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