Eileen, Jackie, and Kathryn needed to find the difference between two angles A1 and A2, that they had drawn on a diagram:
B = A1+A2
They then had to find the cosine of B. Jackie measured A1 to be 50° and A2 to be 3°. But their pencil was kind of dull, so the lines they had drawn were about 0.5° thick. How much uncertainty in each angle was caused by the thick pencil lines? How much uncertainty is there in B? How about the cosine of B?
My work so far:
A1=50°+/- 0.5
A1 max = 50.5. A1 min = 49.5
A2 = 3°+/- 0.5
A2 max = 3.5 A2 min = 2.5
b(max) = 48 and b(min) to be 46
the uncertainty = 47+/- 1
Is this right?
I don't know how to find cosine of B but I think it's cos (0.5) = 1 ?
To find the uncertainty in each angle caused by the thick pencil lines, you correctly added and subtracted 0.5° to the measured values of A1 and A2. So, the uncertainty in A1 is ±0.5°, with a maximum value of 50.5° and a minimum value of 49.5°. Similarly, the uncertainty in A2 is ±0.5°, with a maximum value of 3.5° and a minimum value of 2.5°.
To find the uncertainty in angle B, you need to combine the uncertainties of A1 and A2. Since B is the sum of A1 and A2, you add the maximum uncertainties to get the maximum value of B and subtract the minimum uncertainties to get the minimum value. Therefore, B has an uncertainty of ±1°, with a maximum value of 53.5° (50.5° + 3.5°) and a minimum value of 47.5° (49.5° + 2.5°).
Now, let's calculate the cosine of B. The cosine of an angle is calculated by dividing the length of the side adjacent to the angle by the length of the hypotenuse in a right triangle. However, since we only have the angle value and not any side lengths, we cannot directly calculate the cosine of B.
It seems that you mentioned cos(0.5), but it's unclear what this angle represents in relation to B. If you provide more information about the context or the specific formula you are using, I can help you calculate the cosine of B.