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**John888** A V-gauge is used to find the diameters of pipes. The advantage of such a device is that it is accurate and rugged, and has no moving parts to break down. 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. The line VP is calibrated by listing the corresponding diameters as its units. 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 the formula for d in terms of VP.

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

Please see attachment. P in the attachment, is shaded, and is between B and V.

Thank you.