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Trigonometry for AC Circuits
23 questions By Tony R. Kuphaldt
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Question 16 of 23
The Pythagorean Theorem is used to calculate the length of the hypotenuse of a right triangle given the lengths of the other two sides:
Manipulate the standard form of the Pythagorean Theorem to produce a version that solves for the length of A given B and C, and also write a version of the equation that solves for the length of B given A and C.
Reveal answerStandard form of the Pythagorean Theorem:
$$C = \sqrt{A^2 + B^2}$$
Solving for A:
$$A = \sqrt{C^2 - B^2}$$
Solving for B:
$$B = \sqrt{C^2 - A^2}$$
Notes:The Pythagorean Theorem is easy enough for students to find on their own that you should not need to show them. A memorable illustration of this theorem are the side lengths of a so-called 3-4-5 triangle. Don’t be surprised if this is the example many students choose to give.
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Question 17 of 23
A rectangular building foundation with an area of 18,500 square feet measures 100 feet along one side. You need to lay in a diagonal run of conduit from one corner of the foundation to the other. Calculate how much conduit you will need to make the run:
Also, write an equation for calculating this conduit run length (L) given the rectangular area (A) and the length of one side (x).
Reveal answerConduit run = 210 feet, 3.6 inches from corner to corner.
Note: the following equation is not the only form possible for calculating the diagonal length. Do not be worried if your equation does not look exactly like this!
$$L = \frac{\sqrt{x^4+A^2}}{x}$$
Notes:Determining the necessary length of conduit for this question involves both the Pythagorean theorem and simple geometry.
Most students will probably arrive at this form for their diagonal length equation:
$$L = \sqrt{x^2+ (\frac{A}{x})^2}$$
While this is perfectly correct, it is an interesting exercise to have students convert the equation from this (simple) form to that given in the answer. It is also a very practical question, as equations given in reference books do not always follow the most direct form, but rather are often written in such a way as to look more esthetically pleasing. The simple and direct form of the equation shown here (in the Notes section) looks “ugly” due to the fraction inside the radicand.
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Question 18 of 23
Evaluate the length of side x in this right triangle, given the lengths of the other two sides:
Reveal answerx = 10
Notes:This question is a straight-forward test of students’ ability to identify and apply the 3-4-5 ratio to a right triangle.
