Tuesday, August 21, 2012

Problem of the Week Day 2: Week of 8/20/12 - 8/24/12

Today is day 2 of the problem of the week. Remember to use yesterday's answers in today's problem.

Easy: For this problem, you will need to bring up yesterday's problem as well. Look at the matrix from yesterday and find the highest number there. Let's call that number g.

g =

Now, find the second highest number in the matrix. Let's call that number s.

s =

Finally, find the average of all of the numbers in the matrix. Round that to the nearest hundredth. That number will be called m.

m =

Now that we have those, we can begin the problem. Take a right triangle with the following side lengths. All of the measurements are in millimeters.

a = sgm + x
b = ___
c = y

Try to determine the length of b.

b =

Hard: This problem is trigonometric, but is also a real world problem. For my science fair experiment in 2011, I had to solve almost the same exact problem and it was actually really cool to see the real world application of trigonometry. I hope you find the applications of trigonometry as cool as I did while you complete this word problem. Before you begin, complete these two calculations:

f = x + (a + b)/(y + z)
f =

g = x + a + b
g =

Now for the fun part. Say you need to create a wooden ramp that is f meters long and is propped at an a° angle. You will prop it up with another piece of wood g centimeters up from the bottom and you want the support to make it an a° angle ramp. How many centimeters long should your support be to achieve this angle? Round to the nearest centimeter.

s =