3.Kelly borrowed $16.30 from her
1 answer:
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Step-by-step explanation:
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Answer:
5. 88.0°
6. 13.0°
7. 52.4°
8. 117.8°
Step-by-step explanation:
For angle A between sides b and c, the law of cosines formula can be solved to find the angle as ...
A = arccos((b² +c² -a²)/(2bc))
When calculations are repetitive, I find a spreadsheet useful. It doesn't mind doing the same thing over and over, and it usually makes fewer mistakes.
Here, the side opposite x° is put in column 'a', so angle A is the value of x. The order of the other two sides is irrelevant.
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<em>Additional comment</em>
The spreadsheet ACOS function returns the angle in radians. The DEGREES function must be used to convert it to degrees. The formula for the first problem is shown here:
=degrees(ACOS((C3^2+D3^2-B3^2)/(2*C3*D3)))
As you can probably tell from the formula, side 'a' is listed in column B of the spreadsheet.
The spreadsheet rounds the results. This means the angle total is sometimes 179.9 and sometimes 180.1 when we expect the sum of angles to be 180.0.
Let's call the side of the square
When we cut out the square from each corner, the base of the box is
and the height of the box is of course so the volume is
Approximately, x≈5.70577 or x≈21.294
x can't be bigger than half of 27, so we reject the second value.
We check the second derivative; a negative second derivative indicates a local maximum.
Good. For our answer we want
Answer: 3787.9951 cubic inches