A V-gauge is used to find the diameters of pipes. Look at the figure in the attachment, the measure of angle AVB is 54°. A pipe is placed in the V-shaped slot and the distance VP is used to predict the diameter.

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

The line VP is calibrated by listing the corresponding diameters as its units. This, in effect, establishes a function between VP and d.

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