To find the length of the arm that connects the center of gear A to the center of gear C, we can use the law of cosines.
Let's label the length of the arm as x.
According to the law of cosines, we have:
x^2 = A^2 + C^2 - 2AC*cos(<CAB)
where A = 5 cm, C = 6 cm, and <CAB = 37 degrees.
x^2 = (5 cm)^2 + (6 cm)^2 - 2(5 cm)(6 cm)*cos(37 degrees)
x^2 = 25 cm^2 + 36 cm^2 - 2(30 cm^2)*cos(37 degrees)
x^2 = 25 cm^2 + 36 cm^2 - 60 cm^2*cos(37 degrees)
x^2 = 25 cm^2 + 36 cm^2 - 60 cm^2*cos(37 degrees)
x^2 = 25 cm^2 + 36 cm^2 - 60 cm^2*cos(37 degrees)
x^2 = 25 cm^2 + 36 cm^2 - 60 cm^2*(0.7986)
x^2 = 25 cm^2 + 36 cm^2 - 47.916 cm^2
x^2 = 13.084 cm^2
Taking the square root of both sides, we have:
x = √(13.084 cm^2)
x ≈ 3.62 cm
Therefore, the length of the arm that connects the center of gear A to the center of gear C is approximately 3.62 cm.
Three circular gears with radius A = 5 cm, B = 2 cm and C = 6 cm are shown.
If <CAB = 37o, how long would the arm need to be that connects the centre of gear A to the centre of gear C?
1 answer