Download Geometry Performance Task 1. A bookcase fits diagonally into the

Geometry
Performance Task
1. A bookcase fits diagonally into the corner of a room. The front of the
bookcase is 54 inches wide. Each side of the bookcase uses the same
amount of wall space.
a) What angles are formed where the front of the bookcase touches the
walls?
b) Calculate how much wall space each side of the bookcase uses.
2. A farmer is building a pen inside a barn. The pen will be the shape of a
right triangle. The farmer has 14 feet of barn wall to use for one side of
the pen and wants another side of the pen to be 15 feet long.
a) How many different lengths for the third side are possible? Explain.
b) To the nearest tenth of a foot, find all possible lengths for the third side
of the triangle. Show your work.
c) The farmer wants the area of the pen to be as large as possible. What
length should he choose for the third side? Justify your answer.
d) Find the measure of the acute angles for the triangle you described in
part (c). Round to the nearest degree.
3. At 6 A.M., the angle of elevation of the sun from the horizon is 0
degrees. At noon, the angle of elevation of the sun is 87 degrees. At some
time before noon, a flagpole 50 feet tall casts a shadow 24 feet 9 inches
long. To the nearest minute, what is the time? Explain your work.
Assume the angle of elevation of the sun increases at a constant rate.