25. The Law of Sines (a) A satellite orbiting Earth passes directly overhead at observation stations in Pheonix and Los Angeles, 340 mi apart. At an instant when the satellite is between these two stations, its angle of elevation observed at Los Angeles is 60°. If the distance from the satellite to Pheonix is known to be 170/6 mi, find the angle of elevation observed at Pheonix. (b) To find the distance across a river, a surveyor chooses points A and B, which are 280 ft apart on one side of the river. She then chooses a reference point C on the opposite side of the river and finds ZBAC = 60° and ZABC = 75°. Find the distance from point B to C. (c) Assume you have a triangle AABC with a = 5, 6 = 5/2 and the angle ZA = 30°. Find ZB. How many solutions are there? (d) A fire is sighted from stations A and B. The bearing of the fire from station A is S 60° E, and the bearing from station B is S 30° W. Station B is 4 miles due east of station A. How far is the fire from station A? (e) Use the Law of Sines to solve for the missing values of the triangle which satisfy the given conditions. (Determine if there are 0, 1, or 2 possible triangles). a = (f) Use the Law of Sines to solve for the missing values of the tirangle which satisfy the given conditions. (Determine if there are 0, 1, or 2 possible triangles). a = = 15/3, 6 = 15, ZB = 30°. 20/2, 6 = 40, ZB = 135°. 25.(a) 75° (b) 140v6ft (c) There are two solutions, ZB = 45° or ZB = 135°. (d) 2/3mi (e) There are 2 triangles possible, one where ZA = 60° and one where ZA = 120°. (f) There is only 1 triangle with ZA = 30°
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
Part C
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