23. (a) A 20 ft ladder leans against a building. The angle between the ground and the ladder is 60°. How high does the ladder reach on the building? (b) From the top of a 200 ft lighthouse, the angle of depression to a ship in the ocean is 30°. How far is the ship from the base of the lighthouse? (c) A 600 ft guy wire is attached to the top of a communications tower. If the wire makes an angle of 60° with the ground, how tall is the communications tower? (d) An airplane is flying at an elevation of 5100 ft directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane and the angle of depression to one car is 30° and to the other is 60°. How far apart are the two cars? (e) An airplane is flying at an elevation of 9000 ft directly above a straight highway. Two motorists are driving cars on the highway, both on one side of the plane. If the angle of depression to one car is 60° and to the other is 45°, how far apart are the cars? 40V3 23. (a) ft 3 (b) 200/3ft (c) 300/3ft (d) 6800/3ft (e) (9000 – 3000v3)ft
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 D and E
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