SOLUTION: QUESTION: Your task is to purchase shingles for the roof. The dimensions of the building are 45 inches long and 25 inches wide. The roof extends 1 foot beyond the wall on the two l

Question 741847: QUESTION: Your task is to purchase shingles for the roof. The dimensions of the building are 45 inches long and 25 inches wide. The roof extends 1 foot beyond the wall on the two long sides, and is flush with the wall on the short side. The roof peaks in the middle, with a pitch of 10 degrees.

A single pack of shingles will cover 5 sq. ft.

1. Determine the number of packs of shingles you would buy under the assumption that everything goes smoothly (i.e., no wasted shingles)
2. Determine the number of packs of shingles you would buy assuming that 5% of the shingles will be wasted due to errors, miscalculations, bad cutting, etc.
Would I be correct if I use this way of solving it?
cos 10 = 12.5/x
length = x+1
width = 45
A = L x W
Total = 2A
then do Total divided by 5 = the # of packets??
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Sound reasoning, but watch the units.
I would call the "width" of each side of the roof, and 45 the "length", but the names do not really matter; the surface area of the roof is calculated as you did, anyway.

The problem is the units. If that building is really 45 inches by 25 inches, it must be a dog house, and the area you calculate will be in square inches.
In that case, since a square foot is

,
you can calculate that one packet of shingles will cover
square inches.

If the building was 45 feet by 25 feet, it may be a small house, and when you calculate your area as it will be in square feet, and dividing by 5, and rounding to the nearest integer will give you the answer.

SUPPLEMENT ON HOW TO USE A CALCULATOR FOR THIS PROBLEM:
To calculate with a calculator, you need to understand how the calculator does its work, because not all calculators will work the same way. I have worked with many different calculators, but it may take me a minute to figure out one I am not very familiar with.
Luckily, most calculators nowadays use versions of what we call "algebraic notation", so we do not have to translate the way we write and think algebra into what used to be called "reverse Polish notation."
If you do not have a scientific calculator, you would need a table of trigonometric functions that would tell you that (rounded).
A scientific calculator (especially one that has a key marked "cos" for cosine) is a great help, but you must understand how to give it your calculation instructions.
Furthermore, a calculator with more features, requires reading a longer manual. For example, you would need to know if the calculator wants you to enter the angle in degrees, or in other units, and that may be complicated enough to require that you read the manual.
For simpler calculations, it may be easier to use a simpler calculator.

SIMPLE CALCULATIONS:
The easiest way to calculate with a calculator is to do it the way you would do it without a calculator: step by step.
For that you would first find that is approximately and would write down (or memorize) that number.
Next, you would divide 12.5 by , keying in "12.5 � 0.984808 =" to get

You do not need to write down that or clear the calculator's display, because you can immediately key in "+1=" to get the result

You do not need to write down that or clear the calculator's display, because you can immediately multiply that by 2 and by 45 (or just multiply once, times 90).
To multiply times 90, with the 13.69283 result still in the display, just key in "� 90 ="

CALCULATING COSINE WITH THE CALCULATOR:
To calculate , one calculator may want you to enter the angle first and then press the "cos" key. Another calculator may require you to press the "cos" key before entering the angle. They may or may not require you to enter brackets around the angle value, but you most likely will need to enter either an "=" sign or a ")" after the angle.
It could be worse. I have a TI-34 II that has no "cos" key for just cosine, and it makes me punch in "2nd trig right-arrow right-arrow enter" before the angle to calculate cosine.
On top of that, there is the issue of the units the angle is measured in.
I try "30 sin" first. If it gives me an error message, the calculator must want me to press "sin" first, before the angle.
Looking at the display for feedback, I try pressing "sin 30 =" to see if it needs me to type the parentheses.
When I get my answer, if it is , I know that the calculator is interpreting the angle as being in degrees.
If it is , I know that the calculator is interpreting the angle as being in radians, and I have to figure how to switch to reading angles in degrees. There could be a mode switch, or a "Mode" key to do that, and it could be complicated.

THE COMPLICATED DETAILS:
If you wanted to enter all at once into the calculator, the keystrokes could be something like
"2 � 45 � ( 12.5 � + 1) =" with the part keyed in as your calculator wants it.
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