Math trigonometry problems

Trigonometry is a branch of mathematics. Trigonometry is coined from the Greek words tri + gon + metry.  That means, three + angles + measures. From that we can see that in trigonometry we study about the measures of angles of a triangle. Usually to solve trigonometry problems, refers to finding the sides and angles of a triangle. A triangle as we know would have 3 sides and 3 angles.

Trigonometry gives us a relation between these sides and angles. In practice if we know any 3 of the six parts of a triangle (3 sides and 3 angles = total 6 parts) then we can find the remaining three parts of the triangle using trigonometry.

In schools, trigonometry is usually covered under pre calculus. It finds huge application in science subjects such as physics and organic chemistry. Trigonometry is applicable in study of co-ordinate geometry, conic sections like, circle, ellipse, parabola and hyperbola. The most common application of trigonometry would be in solving heights and distances type of problems. These type of problems, occur very frequently in our daily life, in construction work, in depth estimation of seas and lakes, in the use of radar to locate airplanes, etc.

It is because of these varied applications, that trigonometry is taught at school level itself.

Example trigonometry problems:

The following type of problems can be solved using trigonometry.
(1) A ship sends a signal to a submarine. The depth of the submarine is known and the angle of the signal is read from the signaling machine. Then the distance between the ship and the submarine can be calculated using trigonometry.
(2) A person is viewing a tall tower from a distance. If the height of the tower is known, and the angle of elevation of the top of the tower from the line of sight of the person is also known, then the distance between the person and the tower can be calculated using trigonometry.
(3) If two ships or air planes leave from the same point but in different directions. Then the distance between them at any point of time can be found if their respective bearings are known using trigonometry.

The basic concept of trigonometry is that, that the ratios of sides of angles of triangles with congruent angles are equal. In other words, we know that if two triangles have congruent angles, then the two triangles are said to be similar. The sides of similar triangles are proportional. Trigonometry is based on these concepts.

Statistics: The study of numbers in your life

Introduction to Statistics

Every day we come across a lot of information of facts, numerical figures, tables, graphs etc. These are provided by newspapers, magazines, television and other means of communication. They may relate to cricket batting or bowling averages, profit of companies, temperatures of cities, and so on. These facts or figures, which are numerical or otherwise, collected for definite purpose is called data. Every part of our lives utilizes data in one form or the other. So, it becomes essential for us to extract meaningful information from such data. This extraction of meaningful information is studied in a branch of Mathematics called Statistics.

Statistics deals with collection, analysis, interpretation, and presentation of masses of numerical/ categorical data. It is a way of reasoning together with collection tools and methods designed to help us understand data and information about the world.
Statistics in Everyday Life Today’s society basically depends upon the crunching numbers. The numbers seem to appear everywhere we turn to, from the novels and newspaper articles focused on crime rates to the normal life span of a person who depends upon fast food and then the rating of President’s approval.

On any particular day, one might run into six, seven or more different patterns of statistics. One might come across these variations and literally hordes of statistics in reports by just reading the Sunday newspaper all the way through, advertisements, and various articles covering everything from coffee to the types of nuts.

Importance of Statistics
Statistics plays a vital role in every field of human activities. Statistics has important role in determining the existing position of per capita income, unemployment, housing, etc in a country. Statistics holds a central position in almost every field like Science, Engineering, Economics, Astronomy, Banking  etc, so applications of statistics is very wide. Let us understand the application of Statistics for Scientists and Engineers: Data analyses, experimental design, risk/survival analyses and theoretical concepts are necessary in solving more than one current engineering problem, and in certain cases some of them are need to a greater extent according to the specialty. Solve all your math problems with me. Please comment on my articles.

To continue completing in different markets, the industry should improve the product and service quality. The efforts in statistics helps scientists and engineers to design and develop new products and to improve the ones already existing.  For any natural sciences, experimentation is very important. For the precise measurement of results, their tabulation, that is, recording and comparison is required which is nothing but a form of statistics. This is where Statistics for Scientists plays a vital role.

Box and Whisker Plot

As the name suggests, Box and Whisker Plot consists of a box (rectangular) and two lines extending from the edge of the box on the either sides of the box called the whiskers, whiskers because they resemble the whiskers of a cat. The graph looks something like the one given below,

In statistics, when describing a set of data, without listing all the values, we can use measures of location such as mean and median. Let us understand what Median is, Median is the middle value in a list of data arranged from the smallest to greatest.  A Box and Whisker Plot is dependent on median.

Data is examined using the Five statistical summary or five number summary
1. Minimum (lower extreme)
2. Maximum (upper extreme)
3. Median (second quartile-50th percentile)
4. First quartile (25th percentile)
5. Third quartile(75th percentile)
You might wonder what quartile is, we know that median of a data separates the given data into two equal parts. Quartiles separate the original set of data into four equal parts (quarter is ¼). Quartiles are the percentiles that divide the data into fourths.

A five statistical summary can be represented in a graphical way using the Box and Whisker Plot. The first and the third quartiles are outside the rectangular box, the median is indicated with a vertical line inside the box, and the lower extreme and upper extreme are at the ends of the whiskers.

Box and Whisker Plot Definition:
So, Definition of Box and Whisker Plot or Box and Whisker Definition is the graphical representation that summarizes data using box and whiskers format to show the minimum and maximum values (ends of the whiskers), inter-quartile range (length of the box), and the median(denoted by the vertical line inside the box)
Using Box and Whisker Plot examples, let us now learn How to Make a Box and Whisker Plot


The following data is the amount of marbles fifteen boys own
98, 17, 34, 52, 61, 59, 78, 54, 85, 91, 27, 68, 96, 93, 76
Step1: Arrange the given data in the ascending order or the numerical order
17, 27, 34, 52, 54, 59, 61, 68, 76, 78, 85, 91, 93, 96, 98
Step2: find the median, the median is the value exactly in the middle of an ordered set
68 is the median (second quartile)
Step3: Now, consider only the values which are left to the median.17, 27, 34, 52, 54, 59,61
We now find the median of this list. 52 is the median, which is the first quartile
Step4:Now, consider only the values which are right to the median. 76,78,85,91,93,96,98.
           The median of this list is 91, which is the third quartile.
Step5: Now, we find the extreme. The lowest value in the list 17 is the lower extreme and the greatest
value in the list 98 is the upper extreme.
 let us graph the Box and Whisker Plot using the values,