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Math 577 HW 6
Due Tuesday, Oct 19th, 2010
Solve the following and explain your reasoning.
1. Find x and y.
2. Is ∆BAK ~ ∆JOL ? Why or why not?
3. Jorge, who is 1.7 meters tall, wants to find the height of a tree. From the tree’s base, he walks
12 meters along the tree’s shadow until his head is in a position where the tip of his shadow
exactly overlaps the end of the tree’s shadow. If he is now 6 meters from the end of the
shadows, how tall is the tree? (adapted from Discovering Geometry)
4. Starting from the fact that an equilateral triangle has three equal angles, calculate sin(30o),
sin(60o), cos(30o) and cos(60o).
5. Consider quadrilaterals A, B and C. Using the definition of similar polygons from class
(corresponding angles equal, corresponding sides multiplied by the same constant), show that
if A is similar to B and B is similar to C, then A is similar to C.
6. Let’s call a pentagon equilateral if it has all equal sides. Given an example of two equilateral
pentagons that are not similar to each other.