A = 15 ; b =____________ ; c = 17
1 answer:
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The law of cosines can be helpful here. The largest angle (C) will be opposite the longest side (c). That law tells us ...
... c² = a² + b² -2ab·cos(C)
Then
... cos(C) = (a² +b² -c²)/(2ab)
We don't actually need the angle. We only need to know the sign of the cosine.
... cos(C) = (7² +15² -17²)/(2·7·15) = -15/210 . . . . negative sign, so C > 90°
The sail has the shape of an obtuse triangle.
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A triangle solver app on your calculator, phone, tablet, or computer can give you the result easily.
So basically, think of a ratio as a fraction for these problems. You see the 2 numbers and you put the first one as the numerator and the second as your denominator. For example:
5 to 10
We would change this into:
Because the problem says to simplify, we can divide both sides by 5 and simplify it into:
If the problem says 5:10 instead of "5 to 10" it's the same problem just with different wording. If the numbers are labeled, the you can write the labels next to the number it corresponds with.
If you have any questions, feel free to ask down in the comments, I'll be happy to work with you!
5 to 10
We would change this into:
Because the problem says to simplify, we can divide both sides by 5 and simplify it into:
If the problem says 5:10 instead of "5 to 10" it's the same problem just with different wording. If the numbers are labeled, the you can write the labels next to the number it corresponds with.
If you have any questions, feel free to ask down in the comments, I'll be happy to work with you!