Solution of Triangles
Tags: Engineering Entrance  |  JEE Main  |  CBSE Board  |  JEE Main & Advanced  |  Trigonometry  |  Class 11  |  Class 12
  « Back to Content

Solution of Triangles

Every triangle has 3 angles and 3 sides. Given any 3 quantities out of 3 angles and 3 sides (at least one of which is a side) are given then remaining 3 can be found , which is termed as solution of the triangle. Many interesting relation among these quantities will be discussed in this section. Which formula is to be used where is a very important point here, as a use of wrong formula might lead to large calculations. So be prepared to see some very interesting stuff.



Side AB , BC, CA of a DABC are denoted by c, a, b respectively and is semi perimeter of the triangle and D denotes area of the triangle.

Since Rule:



                        Fig (1)

Draw AD perpendicular to opposite side meeting it in point D.


Þ AD = cSinB


Þ AD = bSinC

Equating 2 values of AD we get

cSinB = bSinc

Similarly drawing a perpendicular line from B upon CA we have

Illustration 1:

Given that ÐB=30, C=10 and b=5 find the angles of A and C of triangle.


Fig (3)


By using sine rule,

Cosine Rule:





                                                           Fig (4)

Let ABC be a triangle and let perpendicular from A on BC meet it in point D

Now      AB2= AD2+BD2

                     = (BC-CD) 2+ (AC2-DC2)

                     = BC2+CD2-2BC.CD+AC2-DC2

                     = AC2+BC2-2BC.CD                                                     ------------------ (1)


So, equation (1) is now

c2 = b2+a2-2abCosC

Similarly CosA, CosB can be found.


  Electricity and Effect of Current      Centre of Mass      Work Power & Energy      Magnetic Effects of Current      AIEEE 2009 Solutions and Analysis      English Core-XII Sample Test Paper      Function Theory      Basis of Inheritance      dasda      Business Studies -XII Sample Test Paper      Chemical Bonding      Group I A      Integration Theory      Organic Chemistry Basic Concepts      Applications of Derivatives      Informatics Practices (065) Sample Question Paper -III      Inorganic Chemistry Group VI A      Properties of Matter      Heat & Thermodynamics      Disha - Path to Success Series     

Free Sign Up!
Sponsored Ads

Preparing for JEE?

Kickstart your preparation with new improved study material - Books & Online Test Series for JEE 2014/ 2015

@ INR 5,443/-

For Quick Info