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Basics
Published in William Bolton, Engineering Science, 2020
For a triangle for which one angle is 90°, the term hypotenuse is used for the side opposite the 90° angle. Pythagoras’ theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is talking about the area of the squares that are built on each side of the right triangle. Thus, for the triangle shown in Figure 1.14: AC2=AB2+BC2ExampleA right-angled triangle has two sides at right angles to each other and of sizes 4 cm and 3 cm. What will the length of the hypotenuse be?Using Pythagoras’ theorem: Hypotenuse2=44+32=16+9=25Therefore, the hypotenuse is the square root of 25 and so 5 cm.
What is a Loudspeaker?
Published in Douglas Self, Audio Engineering Explained, 2012
However, despite the resistance and reactance in the circuit both being equal at 100 ohms, the total impedance (resistance plus reactance) would not be 200 ohms. The same current would flow through both components, but whereas the voltage across the resistor would be in phase with the current, the voltage across the capacitor would be 90 degrees out of phase with the current. We can draw a right-angled triangle, as in Figure 11.9, with one side representing the resistance and the other side, at 90 degrees, representing the reactance. The total impedance (Z) would be represented by the hypotenuse. From Pythagorus' theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore:
Recognizing the Correlation of Architectural Drawing Methods between Ancient Mathematical Books and Octagonal Timber-framed Monuments in East Asia
Published in International Journal of Architectural Heritage, 2023
The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides. Accordingly, the Song Yingzao Fashi’s Building Standards adopt the method of finding the hypotenuse from a right-angled triangle. Thus, the base length of the deleted triangle for drawing an octagon from a square is slightly shorter than the side length of the octagon (Liu 2014, 66). This discrepancy indicates that the theorem does not cover the equilateral octagons defined by modern mathematics [Figure 4].