oblique triangle

(noun)

A three-sided shape that does not contain a $90^{\circ}$ angle.

Examples of oblique triangle in the following topics:

  • The Law of Sines

    • The law of sines can be used to find unknown angles and sides in any triangle.
    • A right triangle contains a $90^{\circ}$ angle, while any other triangle is an oblique triangle.
    • Solving an oblique triangle means finding the measurements of all three angles and all three sides.
    • To solve an oblique triangle, use any pair of applicable ratios from the law of sines formula.
    • The sides of this oblique triangle are labeled a, b, and c, and the angles are labeled $\alpha$, $\beta$, and $\gamma$.

  • The Law of Cosines

    • The Law of Cosines defines the relationship among angle measurements and side lengths in oblique triangles.
    • Thus, for right triangles, the Law of Cosines reduces to the Pythagorean theorem:
    • Substitute the values of $a$, $c$, and $\beta$ from the given triangle:
    • An oblique triangle, with angles $\alpha$, $\beta$, and $\gamma$, and opposite corresponding sides $a$, $b$, and $c$.
    • This oblique triangle has known side lengths $a=10$ and $c=12$, and known angle $\beta = 30^{\circ}$.

  • Episiotomy

    • It can be further divided into the urogenital triangle in front and the anal triangle in back.
    • Therefore, the oblique technique is often applied.
    • In the oblique technique, the perineal body is avoided, cutting only the vagina epithelium, skin and muscles (transversalius and bulbospongiosus).
    • This technique bifurcates the perineal body, which is essential for the integrity of the pelvic floor. 2)The oblique technique, the perineal body is avoided, cutting only the vagina epithelium, skin and muscles

  • Cervical Plexus

    • The branches of the cervical plexus emerge from the posterior triangle at the nerve point, a point that lies midway on the posterior border of the sternocleidomastoid.
    • The transverse cervical nerve (superficial cervical or cutaneous cervical) arises from the second and third cervical nerves, turns around the posterior border of the sternocleidomastoideus about its middle, then passes obliquely forward beneath the external jugular vein to the anterior border of the muscle, where it perforates the deep cervical fascia and divides beneath the platysma into ascending and descending branches that are distributed to the antero-lateral parts of the neck.
    • They emerge beneath the posterior border of the sternocleidomastoideus, and descend in the posterior triangle of the neck beneath the platysma and deep cervical fascia.

  • Right Triangles and the Pythagorean Theorem

    • A right triangle is a triangle in which one angle is a right angle.
    • If the lengths of all three sides of a right triangle are whole numbers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.
    • It defines the relationship among the three sides of a right triangle.
    • Example 2:  A right triangle has side lengths $3$ cm and $4$ cm.  
    • Use the Pythagorean Theorem to find the length of a side of a right triangle

  • How Trigonometric Functions Work

    • Trigonometric functions can be used to solve for missing side lengths in right triangles.
    • We can define the trigonometric functions in terms an angle $t$ and the lengths of the sides of the triangle.
    • The hypotenuse is the side of the triangle opposite the right angle, and it is the longest.
    • The trigonometric functions are equal to ratios that relate certain side lengths of a  right triangle.  
    • The sides of a right triangle in relation to angle $t$.

  • Trigonometric Functions

    • Trigonometric functions are functions of an angle, relating the angles of a triangle to the lengths of the sides of a triangle.
    • They are used to relate the angles of a triangle to the lengths of the sides of a triangle.
    • Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.
    • Note that this ratio does not depend on size of the particular right triangle chosen, as long as it contains the angle $A$, since all such triangles are similar.
    • If two right triangles have equal acute angles, they are similar, so their side lengths are proportional.

  • Horizontal Asymptotes and Limits at Infinity

    • The asymptotes are computed using limits and are classified into horizontal, vertical and oblique depending on the orientation.
    • They can be computed using limits and are classified into horizontal, vertical and oblique asymptotes depending on the orientation.
    • Oblique asymptotes are diagonal lines so that the difference between the curve and the line approaches $0$ as $x$ tends toward $+ \infty$ or $- \infty$.
    • More general type of asymptotes can be defined as the oblique asymptote case.

  • Anterior Muscles

    • They are continuous with the external oblique muscle of the abdomen.
    • External Oblique – The external oblique is the largest and most superficial of the flat muscles.
    • Internal Oblique – Lying deep to the external oblique, the internal oblique is smaller and thinner.
    • Its fibers run perpendicular to the external oblique, improving the strength of the abdominal wall.
    • Highlighted in orange, the external obliques lie inferior to the pectoral muscles

  • Asymptotes

    • There are three kinds of asymptotes: horizontal, vertical and oblique.
    • An asymptote that is neither horizontal or vertical is an oblique (or slant) asymptote.
    • A rational function has at most one horizontal or oblique asymptote, and possibly many vertical asymptotes.
    • The graph of a function with a horizontal ($y=0$), vertical ($x=0$), and oblique asymptote (blue line).
    • Explain when the asymptote of a rational function will be horizontal, oblique, or vertical