A V-gauge is used to find the diameter of a pipe. The advantage of such a device is that it is rugged, it is accurate, and it has no moving parts to break down. In the figure, the measure of angle AVB is 54°. A pipe is placed in the V-shaped slot and the distance VP is used to estimate the diameter. The line VP is calibrated by listing as its units the corresponding diameters. This, in effect, establishes a function between VP and d.

a) Suppose that the diameter of a pipe is 2 cm. What is the distance VP?

b) Suppose that the distance VP is 3.93 cm. What is the diameter of the pipe?

c) Find a formula for d in terms of VP.

d) Find a formula for VP in terms of d.

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V. 2. P A B