Tree Stand Ladder Sticks
Problem Solving Help for 7th grade math?
Marissa's cat is stuck in a tree. The cat is on a branch 23 feet from the ground. Marissa is 5.5 feet tall, and she owns a 16-foot ladder.
a) Create a table that shows how high up on the tree the top of the ladder will reach if Marissa places the base of the ladder 1 foot, 2 feet, 3 feet, 4 feet, and 5 feet from the base.
b) How high will Marissa be if she places the base of the ladder the distances from the tree in part a, and stands on the rung 2.5 feet from the top of the ladder?
c) Do you think Marissa can use the ladder to reach her cat? Explain your reasoning.
a) Set up triangles where the hypotenuse is 16ft (the ladder) and one of the two edges are 1, 2, 3, 4, 5ft (the base of the ladder). Use a^2 + b^2 = c^2 where a is the base length, c is the hypotenuse and b is the value you are trying to find.
Ex w/ 1ft base:
1^2 + b^2 = 16^2
1 + b^2 = 256
b^2 = 255
b = 15.97ft.
b) Simply take your answers from part a) and add 5.5ft (the height of the girl) to them.
Ex w/ 1ft base:
15.97ft + 5.5ft = 21.47ft
c) Using logic here think about it. Let's take the 1ft base as the example. Marissa standing on top of the ladder is 21.47ft. That's clearly not high enough to reach the cat . . . but what happens if Marissa reaches upwards. As long as her arms can reach roughly 1.53ft above her head she should be able to reach it.
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