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 denote the length of the arm as x.
According to the law of cosines, in a triangle with sides a, b, and c, and angle θ between sides a and b, the following equation holds:
c^2 = a^2 + b^2 - 2ab*cos(θ)
In our case, we have a right-angled triangle formed by the arm, the radius of gear A (5 cm), and the radius of gear C (6 cm). Therefore, the angle θ is 90 degrees.
Plugging in the given values into the equation above, we get:
x^2 = 5^2 + 6^2 - 2 * 5 * 6 * cos(90°)
cos(90°) equals 0, so the equation simplifies to:
x^2 = 5^2 + 6^2 - 0
Calculating:
x^2 = 25 + 36
x^2 = 61
Taking the square root of both sides:
x = sqrt(61)
Therefore, the length of the arm that connects the center of gear A to the center of gear C is approximately 7.81 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