Answer: B. 5/13
This is the same as writing ![\frac{5}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B13%7D)
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Reason:
We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.
a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse
![a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13\\\\](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%20%3D%20c%5E2%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B5%5E2%2B12%5E2%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B25%2B144%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B169%7D%5C%5C%5C%5Cc%20%3D%2013%5C%5C%5C%5C)
The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.
Now we can compute sine of theta
![\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{5}{13}\\\\](https://tex.z-dn.net/?f=%5Csin%28%5Ctext%7Bangle%7D%29%20%3D%20%5Cfrac%7B%5Ctext%7Bopposite%7D%7D%7B%5Ctext%7Bhypotenuse%7D%7D%5C%5C%5C%5C%5Csin%28%5Ctheta%29%20%3D%20%5Cfrac%7B5%7D%7B13%7D%5C%5C%5C%5C)
This points us to choice B as the final answer.
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Extra Info (optional)
- 5/12 is the value of tan(theta) since it's opposite/adjacent
- 12/5 is the value of cot(theta), the reciprocal of tangent
- 12/13 is the value of cos(theta), because cos = adjacent/hypotenuse
-Answer:
4 lbs of 37% mixed nuts
Step-by-step explanation:
![\frac{\left(17+.37x\right)}{17+x}\:=\:.88](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%2817%2B.37x%5Cright%29%7D%7B17%2Bx%7D%5C%3A%3D%5C%3A.88)
x = 4
First, find the digit in the place you are rounding to. Look at the digit one place to the right. If the digit is less than 5, round down. If the digit is 5 or greater, round up.
For example: round 1.86 to the nearest tenth
Look at the tenth digit (8). The number to the right of it is 6. Since it’s above 5, round the 8 up to 9. So you would get 1.9.
If it was 1.84, since 4 is less than 5, you would not round the 8, and you would get 1.8
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