Missing Lengths
Missing Lengths - Related Videos
01:10
Interference: Path Lengths
0 Views •
2023
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same. Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
02:49
Bond Energies and Bond Lengths
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2020
Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, that is, the energy necessary to separate the bonded atoms. Separating any pair of bonded atoms requires energy — the stronger a bond, the greater the energy required to break it. The energy required to break a specific covalent bond in one mole of gaseous molecules is called the bond energy or the bond dissociation energy. The bond energy for a...
01:26
Integration Applied to Polar Coordinates to Find Arc Lengths
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2026
In polar coordinates, a plane curve is described by a radial distance r from a fixed point, called the pole, and an angle θ measured from a reference direction. This system is especially useful for paths that naturally involve rotation, such as an expanding spiral followed by a search drone. If the hiker’s last known position is treated as the pole, then the drone’s location at any instant can be represented by the polar equation r = f(θ), where the distance from the pole changes as the drone...
04:15
Polyacrylamide Gel Electrophoresis: An Analytical Technique to Detect Heparan Sulfates of Varying Chain Lengths Isolated from Mouse Lung Tissue
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2025
This video demonstrates the separation procedure of heparan sulfates isolated from mouse lung tissue using polyacrylamide gel electrophoresis.
09:57
Obtaining Quality Extended Field-of-View Ultrasound Images of Skeletal Muscle to Measure Muscle Fascicle Length
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Cited by 10 •
2020
This study describes how to obtain high quality musculoskeletal images using the extended field-of-view ultrasound (EFOV-US) method for the purpose of making muscle fascicle length measures. We apply this method to muscles with fascicles that extend past the field-of-view of common traditional ultrasound (T-US) probes.
FAQs
For a right triangle, the Pythagorean theorem connects the lengths of its sides through a specific mathematical relationship. If two side measurements are known, substituting them into that relationship creates an equation for the third side. Solving the equation provides the unknown distance, making this approach useful for diagonal measurements and other right-triangle situations.
Similar figures have matching shapes, so corresponding lengths maintain consistent relationships. A known length in one figure can therefore be compared with its corresponding length in another to establish an equation. Solving with the resulting scale relationship allows an unknown dimension to be determined, especially when a diagram contains proportional copies of the same shape.
Each relationship supplies different information about an unknown dimension. Perimeter connects the total boundary distance to individual sides, while area relates the amount of enclosed space to measurements of the figure. Angle relationships can constrain side arrangements or triangle properties. Choosing the relationship that matches the available data prevents irrelevant or incomplete calculations.
Algebra converts visual information into a solvable equation. First, a diagram's known measurements and geometric relationships are represented symbolically, with the unknown assigned a variable. The equation is then rearranged to isolate that variable. This translation is important because a visually clear diagram may still require algebraic reasoning to produce an exact measurement.
Begin by identifying the unknown and listing the measurements already provided. Next, select the relevant relationship, such as the Pythagorean theorem, similarity, perimeter, area, or angle properties. Substitute the known values, solve the resulting equation, and check whether the answer fits the diagram and its units. This workflow connects visual interpretation with quantitative verification.
The same reasoning supports practical calculations in architecture, engineering, surveying, and design. A worker or designer can use known dimensions and geometric relationships to determine an unmeasured distance or component size. The resulting value helps interpret plans, analyze spatial arrangements, or guide construction and design decisions where direct measurement may be difficult.
Solving unknown dimensions builds a connection between geometry, algebra, and quantitative reasoning. Students practice interpreting spatial information, selecting a mathematical model, and evaluating whether a result is reasonable. These habits provide preparation for trigonometry, spatial analysis, and more advanced mathematical modeling, where geometric relationships continue to describe and predict measurable quantities.