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The angle of the intersection with the green plane is the red plane's apparent dip in the northward direction . When measuring or describing the attitude of an inclined feature, two quantities are needed. The angle the slope descends, or dip, and the direction of descent, which can be represented by strike or dip direction. [4]
Given triangle sides b and c and angle γ there are sometimes two solutions for a. The theorem is used in solution of triangles , i.e., to find (see Figure 3): the third side of a triangle if two sides and the angle between them is known: c = a 2 + b 2 − 2 a b cos γ ; {\displaystyle c={\sqrt {a^{2}+b^{2}-2ab\cos \gamma }}\,;}
Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA) A side, the angle opposite to it and an angle adjacent to it (AAS). For all cases in the plane, at least one of the side lengths must be specified. If only the ...
Case 1: three sides given (SSS). The cosine rule may be used to give the angles A, B, and C but, to avoid ambiguities, the half angle formulae are preferred. Case 2: two sides and an included angle given (SAS). The cosine rule gives a and then we are back to Case 1. Case 3: two sides and an opposite angle given (SSA). The sine rule gives C and ...
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.
Take a hyperbolic plane whose Gaussian curvature is .Given a hyperbolic triangle with angles ,, and side lengths =, =, and =, the following two rules hold.The first is an analogue of Euclidean law of cosines, expressing the length of one side in terms of the other two and the angle between the latter:
Putting any of the four vertices in the role of O yields four such identities, but at most three of them are independent; if the "clockwise" sides of three of the four identities are multiplied and the product is inferred to be equal to the product of the "counterclockwise" sides of the same three identities, and then common factors are ...
A depression position finder measured the range to a distant target (such as a ship) by solving a right triangle in which the short side was the height of the instrument above mean low water; one angle was the constant right angle between the short side and the plane of the ocean, and the second angle was the depression angle from the horizontal of the instrument as it sighted down from a fire ...