Transversal Angles

Transversal Angles : - Once a transverse line intersects 2 or a lot of parallellines, then the angles that area unit fashioned area unit known as the transverse angles. We’ve already studied the properties of the transverse angles within the decussate line topics. The intersection of 2 lines indicates that 2 lines coincide or meet at one purpose.

During this condition the slopes of the 2 lines area unit reciprocal to every different. The cross suggests that to chop or to fulfill at any purpose. The road that intersects 2 or a lot of lines at distinct points is termed a transverse line. The decussate lines are also oblique, perpendicular, traversal or parallel lines. Any figure is often drawn by the assistance of the decussate lines. Every type of triangle, parallelograms and prism are often created by these lines. Interior angles on identical facet of the transverse also are noted as consecutive interior or allied or co-interior angles. Repeatedly we tend to use the words alternate for alternate interior.

Letter of the alphabet angle is very important to seek out the intersections of 2 or a lot of lines.  = Tan –1 (m1 - m2) / (1 + money supply m2). There are a unit cases which may be judged by this formula. Initial case is once money supply and money supply area unit equal then letter of the alphabet is up to tan inverse zero. Letter of the alphabet is up to zero. Once the angle is zero then 2 lines area unit parallel to every different. The second case arises from the very fact that once one in the entire 2 slope area unit reciprocal to every different. During this case the divisor of the formula becomes zero.

Something divided by zero is up to eternity. Tan inverse eternity is up to ninety degree. Letter of the alphabet is up to ninety degree. Thus each the lines area unit perpendicular to every different. thus the subsequent 2 conclusion are often written as (i)Two straight lines area unit parallel if money supply = money supply (ii) 2 straight lines area unit perpendicular, if m1.m2 = -1

Special Angles : - Special angles area unit the pure mathematics angles like thirty, 45, and sixty degrees. Trigonometrical Ratios of some customary Angles area unit given below. 

Trigonometrical ratios of angle thirty deg

Sin thirty deg = ½

Cos thirty deg = (√3)/ (2)

Tan thirty deg =1/ (√3)

Cot thirty deg = √3

Cosec thirty deg = two

Sec thirty deg = (2)/ (√3)

Measurement of Angle in Radian; in system of measurement, the length of the circumference of a circle continuously bears a relentless ration to its diameter.

Circumference of a circle = 2 pi(radius)

Diameter of a circle

= 3.14159265

= 22/7

180° = two rt angles = pi radians

360° = four rt angles =2pi radians

 /2pi90° = One rt angle = rad

1 rad = one800 / π = 570 17’ forty four.8”

= 57.29577950

Let us notice What should be the radius of circular ring path spherical that Associate in Nursing jock should run five times to explain 1760 mtrs.

In five rounds: 1760 mtrs 1760/5 = 352 m

In one round:

i.e., Circumference = 352 m

Circumference = 2pi radians

Radius =pi Circumference / 2 pi = 352 /2 x 3.14159265 m

= 352 / 2 x pi

= 56 mtrs.

The Probability

Probability is a measure or estimation of the likeliness or likelihood that an event will occur. Probability is used to quantify an attitude of mind towards some proposition of whose truth we are not certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty), we call probability. Thus the higher the probability of an event, the more certain we are that the event will occur. A simple example would be the toss of a fair coin. Since the the 2 outcomes are deemed equiprobable, the probability of "heads" equals the probability of "tails" and each probability is 1/2 or equivalently a 50% chance of either "heads" or "tails".                              Source - Wikipedia

Probability Questions: -   Let us find the prob for each event when a coin is tossed five hundred times and the frequency of the two events is given as Head: Three Hundred, tails = two hundreds.

Solution : - We are given that the total number of trials is five hundred. Therefore, the number of times E happens, i.e., the number of time the head comes up is three hundred.  Therefore the probability of head = the number of head / Total number of the trials Or P (E) = 300/ 500 = 0.6. Similarly the probability of tail = the number of tail / Total number of the trials Or P (F) = 200/ 500 = 0.4. Hence the prob of success is zero point six and prob of failure is zero point four. The point which is to be noted down is that the total sum of both the probability is equal to one.

Example: - Let us find the prob, when the two coins are tossed simultaneously for four hundred and eighty times and we get the following events. Two heads: one hundred and twenty times (120), One head:  Two hundred and three times. (203), No head:  one hundred and fifty seven time (157)

Solution:-  (1) The probability of getting two heads = the total number of heads divided by the total number of chances. The probability of getting two heads = 120 / 480 = ¼ = 0.25. The probability of getting one heads = 203 / 480   = 0.42292

The probability of getting no heads = 157 / 480 = 0.32708

We can see that P (E₁) + P (E₂) + P (E₃) = 1, cover all the outcomes of a trial.
Or P (E₁) + P (E₂) + P (E₃) = 0. 25 + 0.42292 + 0. 32708 = 1

Example:- The record of a weather station  shows that the out of past two hundred consecutive days, its weather forecast is correct for one hundred and forty five ( 145)  times. Let us calculate the probability that on a given day it was correct and the probability that on a given day it was not correct.

Solution: - The record of a weather station is available for two hundred consecutive days. The Probability P (E₁) that on a given day the forecast was correct = the number of days when the forecast was correct/ Total number of days for which record is available  Or P (E₁) = 145 / 200 = 0.725. P (E₂) that on a given day it was not correct = 55/200 = 0.275, Notice that P (the forecast was correct + the forecast was not correct) = 0.275 + 0.725 = 1

How do you Find Probability: -The word probably, doubts most probably, chances etc are used to define the uncertainty. The uncertainty of the probably etc can be measured numerically by means of probability. Therefore the probability started with gambling, it has been used extensively in the field of physical sciences, commerce, etc. Let there are n number of trials. The probability of an event E happening, is given by P (E) =
Number of trials in which the event happened / the total number of trials.

Let there are n number of trials. The probability of an event E happening, is given by P (E) = Number of trials in which the event happened / the total number of trials.