[Trigonometry] Introduction, Types of Questions, Shortcut for memorizing 30,45,60 for SSC CGL CDS

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Mrunal Patel is providing free updates to the Economy current affairs, budget & Economic survey for the upcoming UPSC Prelims and Mains under this Win21 Series. In Pillar4C, he'll cover new developments related to GDP, Inflation, Unemployment including latest budget and economic survey!
  1. Introduction
  2. Types of Trigonometry Questions
  3. Trig: Height and Distance


  • From outside, trigonometry may look lengthy, boring, difficult, tedious and frustrating. But it doesn’t change the fact that trigonometry as a topic important for SSC exams (CGL, FCI, CPIO etc.) and CDS exam (Combined defense services).
  • In CGL-2012, at both Tier I and II, there were around 8 questions from Trigonometry alone.
  • Based on the previous SSC papers, I classify the Trigonometry questions mainly into 4 types

Types of Trigonometry Questions

Trigonometry Height & Distance- type of questions

1. Height and distance related
  • Example “String of a kite is 100 metres long and it makes an angle of 60° with the ground. Find the height at which the kite is flying.”
  • Height and distance questions can be further classified into five subtypes, but most of them can be solved pretty easily via “Tan 30, 45 and 60.”
  • The techniques and shortcuts are explained my youtube videos.
2. Table related
  • For example find value of sin430+cos345*cosec260+…something like that.
  • To solve such questions, you’ve to know the sin cos tan cosec sec and cot values of 0, 30, 45, 60 and 90 angles. Again nothing difficult, as long as you know the values.
3. Complementary angles (90-A) related
  • for example find value of tan4 x tan 43 x tan 47 x tan 86.
4. Combo of Trigonometry formulas + Algebra formulas.
  • For example find value of (1+cotA-cosecA)(1+tanA+secA)

Let’s start with the first type: Height and Distance related.

Trig: Height and Distance

These questions can be further classified into five types



1. One building one angle From a ground point that is 400 meters away from a building, the angle of elevation is 30 degrees. Find height of this building.
2. Broken trees and telephone poles A tree breaks down due to storm and its top touches the ground and makes an angle of 30°. If the top of that tree touches the ground 15 m away from the bottom then find the height of this tree
3. One building two angles or two shadows. As angle of elevation of the sun increases from 30° to 60°, Shadow of a building is reduced by 10 m find the height of this building.
4. Two buildings two angles From a 60 m tall building, the angle of depression of the top and the bottom of a tower is 30 and 60° respectively. Find the height of this tower.
5. Find Speed time or distance. A man on the top of building observes a car moving at a uniform speed and coming directly towards the building.  It takes 12 minutes for the angle of depression to change from 30 to 45, how soon after this, will the car reach the building?

In the books, you may have seen a big table containing values of sin cos tan cosec sec and cot for 0, 30, 45, 60 and 90 angles. As far as Height and distance is concerned, there is absolutely no need to mugup that big n boring table because of following reasons

  1. Most of the questions only have 30, 45 and 60 degrees.
  2. And To memorize the values of SIN, COS, TAN, COSEC, SEC and COT for 30, 45, 60, Just remember the Topi TrianglesTM technique. (Explained in following video)

If the video is not visible, check it directly on my youtube channel youtube.com/user/TheMrunalPatel
Above video also contains overview of the Height and Distance Questions and its five subtypes. How to solve each type of height and distance questions, will be explained in depth in separate videos later on. For more [Aptitude] related content, visit the Archive on Mrunal.org/aptitude

55 Comments on “[Trigonometry] Introduction, Types of Questions, Shortcut for memorizing 30,45,60 for SSC CGL CDS”

  1. thank u dear team as always
    attention:its time to start mrunal protocol :-) in https://www.mrunal.org the ocean of gs has just gotten bigger.good for fishes(gs lovers) not for humans(optional lovers).its high time we had a summit here.under mrunal and teams guidance :)

    1. Yes sir, there will be only one optional subject with two papers in the Mains exam from now on so select carefully!!

  2. hi mrunal, i am an avid reader of your articles……..looks funny but the concept is clearly understood……..can you please explain 3 stage nuclear program clearly…….thanks a ton once again…….

  3. Sir, expecting an article on the changed syllabus… hope you will also suggest the source material for new common papers of mains…. thank you

  4. mrunal bhai, dost
    actually not 2 say bt i hav taken a challenge…
    this is for Mr. Mrunal Patel vs coaching institite.
    u knw my frnd used to say that i cn nevrr make it widout coaching n actually boast abt his coaching.
    plz make me a person 2 respond in a genuine way 2 my frnd plz mrunal bhai. thanx plz again plz. i have a blind faith. gn.

    1. well i am no mrunal or a part of his team i vl give my thoughts thought i cant match his clear cut answers:-).
      mrunal doesnt train u.he guides u.training has a limit when ur teacher says u are the best in maths tat makes u feel great bt in reality there is more to learn in maths than u cud ever imagine.in training ur teacher is ur judge.in guidance u r ur own judge.u knw mre abt u than ur teacher.in simple sense tutors train u to look the way they want u to see.u = flocks of sheep.mrunal lets u see the whole world n makes u think.he is better than privates who make truck load of cash.hope i gav a gud replyyy.u watch?mrunalji

  5. sir i want to know that in ias mains exam i have to choose one optional subject with two paper i.e zoology paper 1 and paer 2 OR two optional subjects i.e zoology + public.ad.?PLZ LET ME KNOW THIS?//SOON…

    1. I too had the same confusion but it is now clear: we have to choose only 1 optional subject. earlier i had chosen history and psychology as the 2 optional papers; but now due to the changed pattern i will be choosing psychology only; in your case you, too have to choose only 1 optional subject. if u want to choose zoology then u will have only zoology with 2 papers and NOT pub ad.

  6. hi, mrunal i want you to write up a article on the changed mains pattern and the required strategy for it…..you help will be highly appreciated

  7. Namshkar sir,
    Sir me sambhlyu che k UPSC main ni pattern change
    Tahyi che to sir me BCA karyu che to mare kayo.subject
    Options tarike rakhi sakay???
    Ane tame aana mate strategy banavjo…thank U.

  8. Sir,
    I have a confusion. I know the agg % of my b.tech. But still not got provisional marksheet. It will come in sep-october. So, my doubt is that- Is there require to attach marksheet in mains exam form?
    Plz tell me if anybdy knows…thnx!

  9. how to solve following question?

    A class consists of 100 students; 25 of them are girls and 75 boys; 20 of them are rich and the remaining poor; 40 of them are fair-complexioned. The probability of selecting a fair complexioned rich girl is
    (a) 0.05
    (b) 0.04
    (c) 0.02
    (d) 0.08

    1. i think
      prob. of selecting a girl: 25/100
      prob. of selecting a rich student: 20/100
      prob. of selecting a fair comp. student: 40/100
      prob. of selecting a rich fair girl: 1/4 x 1/5 x 2/5 = 0.02

  10. Mrunal Sir ,
    Please explain us how to solve such a bit tricky questions like………

    Q 1) In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class, has passed in only one subject is:
    1). 13/25
    2). 3/25
    3). 17/25
    4). 8/25

    Q 2) A committee consists of 9 experts taken from three institutions A, B and C, of which 2 are from A, 3 from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is:
    1). 1/729
    2). 1/24
    3). 1/21
    4). 2/7

    1. P(M)= 70-30
      = 40
      P(S)= 55-30
      The probability that a student selected at random from the class, has passed in only one subject is
      = (40+25)/125
      = 13/25


  12. Sir please write on special pwer act(afspa) and civil rights minute detail …it will be great help…thanks


  14. sir while reading any article on ur site i dnt see the date on which article is posted…so its become difficult to have a sense of sequence of events…

  15. hi,
    In my firefox I could not read the instructions for UPSC candidates which is at link http://upsconline.nic.in/download1.php?type=ni&file=INSTR_CSP2013.html
    but when visit that link first time it is is in readable format but now it showing like this page containing following
    ��<�h�t�m�l� �x�m�l�n�s�:�v�=�"�u�r�n�:�s�c�h�e�m�a�s�-�m�i�c�r�o�s�o�f�t�-�c�o�m�:�v�m�l�"� � �x�m�l�n�s�:�o�=�"�u�r�n�:�s�c�h�e�m�a�s�-�m�i�c�r�o�s�o�f�t�-�c�o�m�:�o�f�f�i�c�e�:�o�f�f�i�c�e�"� � �x�m�l�n�s�:�w�=�"�u�r�n�:�s�c�h�e�m�a�s�-�m�i�c�r�o�s�o�f�t�-�c�o�m�:�o�f�f�i�c�e�:�w�o�r�d�"� � �x�m�l�n�s�:�m�=�"�h�

    what's the problem please anybody help…….

  16. Hi sir,
    Please provide the videos in English format. It is difficult to understand in Hindi.Thank you

  17. Yes mrunal sir plz provide videos in English. Some aspirants are hailing from TN so we cant understand Hindi (This really same being unknown national language im sorry abt that).

    1. Well said Anand. But Hindi is not our national language.According to the article 343 (1) of the Constitution of India Hindi in devanagari script is OFFICIAL language of India. But people mistakenly believe that Hindi is our NATIONAL language.India has NO national language.Sorry if i am wrong :)

  18. Sir, Please explain other types of trigonometric questions also, that you have mentioned.
    Table related, 90-A, Trigono+ algebra
    SSC exam is nearby, please upload them ASAP.

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