Part 1
There are many ways to go about this, but one possibility is the following:
You are building a tree house. Your ladder is 10 feet long and the portion in the tree you're trying to get to is 8 feet off the ground. How far should the base of the ladder be from the tree so you can reach that portion?
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Part 2
The drawing is shown below. The diagram is shown in 2D to keep things as simple as possible. Adding a third dimension greatly complicates everything.
We have a right triangle, so it has a 90 degree angle as shown by the square marker. The vertical leg is 8 feet. The horizontal leg is unknown. The hypotenuse (longest side) is 10 feet long to indicate the ladder.
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Part 3
Use the pythagorean theorem to get...
a^2 + b^2 = c^2
x^2 + 8^2 = 10^2
x^2 + 64 = 100
x^2 = 100-64
x^2 = 36
x = sqrt(36)
x = 6
The base of the ladder should be 6 feet away from the tree, so that you can reach 8 feet off the ground.
So, since the student makes $30 each week, we can disregard the number of hours.
So, we can model this situation by the following equation
9.5h+30
So, if he works 10.25 hrs (15 minutes = .25 of 1 hr) we just plug that number in
Since it's money we round to the nearest cent
So he will make $127.28 Next week