2(40)+20 = 100m
40+20= 60m
100x60= 6000m
On your calculator, make sure you're in radian mode, not degree mode, that you are in a trig coordinate plane (do this by hitting "zoom" and choosing ZTrig), and when you enter the function into the "y =", you have to enter it in like this: 7cos(2x)-3. Hit "graph" and you'll see that the wave goes through the x-axis in 4 places within your specified interval. Hit 2nd and "trace" and then "zero". Move your cursor so it's just above the x-axis where the curve goes through and hit enter, then move it so it's just below the x-axis where the curve goes through and hit enter again. Hit enter a 3rd time, and you SHOULD see that your x has a value while y = 0. Do that for all of the places where the curve goes through the x-axis. That's how you find the zeros of a trig curve (or any curve, for that matter) on a calculator. The zeros are the solutions. If this was solvable like a regular equation, using trig identities and right triangles, you wouldn't have to use your calculator. But just like when you go to factor a second degree polynomial and you're having trouble with it you can use the quadratic formula and it's never-fail, neither is your calculator.
Start by calling the shortest side
. We then know that the longer leg (call it
) is 7 feet longer i.e.
. We also know that the hypotenuse,
is 1 foot more than twice the short leg i.e.
. We now have 3 unknowns but only 2 equations to solve them. Luckily we know this is a right triangle so we can use the Pythagorean Theorem as our third equation:
Substituting known values:
This is now an equation in one variable and can be solved algebraically for
. Back-substitution can then be used for the other sides.
