A tapered shaft has a diameter of 5 centimeters at the small end and is 15 centimeters long. If the taper is 3°, find the diameter of the large end of the shaft.
Let's "slice" the shaft in half, cutting through the diameters of the ends, and look at this cross section.
Now we can see that the diameter of the large end = g + g + 5 = 2g + 5
tan θ = opposite / adjacent
tan 3º = g / 15 Multiply both sides of this equation by 15 .
15 tan 3º = g
diameter of large end = 2g + 5 Substitute 15 tan 3º in for g .
= 2(15 tan 3º) + 5
= 30 tan 3º + 5 Put this into a calculator to get....
≈ 6.572 cm