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3) Anastazia is climbing a very steep hill by a path that goes due East. It turns out that the distance she has traveled East (as the crow flies) is the same as her gain in altitude.
Using her GPS receiver she calculates that she has gone 2000 feet directly East. How far has she actually walked straight up the hill? Give an exact answer.
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The figure to the left shows Anastazia's path.
compute Anastazia's path by the pythagorean theorem:
D =
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4) A cube sculpture is made from cubes glued together along their faces. Look at the three views provided of Joe's cube sculpture. After he put it together he painted all
exposed surfaces. How many square faces of the unit cubes did he paint?
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- Strangely, you don't even need to visualize the 3-D structure to count the painted faces because they are twice the exposed faces! (one you see and the other one on the back).
- Total = ____ painted faces.
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5) The triangle ABC shown has the angle measures shown. It is reflected over the line BC. Then the image triangle is reflected over the image of line BA. Keep reflecting the new image triangle over new line segments that have one endpoint at B until you have 12 triangles total all with one vertex at B. Is the resulting shape a polygon and if so how many
sides does it have? If it's not a polygon why isn't it? A sketch can be part of your answer.
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- The angle ABC = _____ degrees.
- Reflecting the triangle around line BC and then the reflected triangle around the reflected line BA results in a folding around a circle.
- With 12 triangles (the original one +11 reflections) makes the total angle at B = ______ degrees.
- The resulting figure ______ a polygon.
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