Calculating Angles in Triangle

 The three lines which are enclosed to form a shape called triangle. The triangle angles can be determined by using the triangle formulas. The angles can be easily determined in the triangles by adding all the angles of the triangle and by using the trigonometry laws. Now we see about the calculating angles in triangles.

 

About Calculating Angles in Triangles:

 

                           The calculating of the angles in triangles can be done by adding all the angles in the given problem or in the figure. The triangle angles can be calculated by means of the trigonometry laws also. The angles of triangle can be calculated by the law of cosine given as follows,

                                  cos A = `(b^2 + c^2 - a^2)/(2bc)`

                                  cos B = `(c^2 + a^2 - b^2)/(2ca)`

                                  cos C = `(a^2 + b^2 - c^2)/(2ab)`

                The angles can be determined with the help of the other angles measurement.

 

Examples on calculating angles in triangles:

 

                        Now we see calculating the angles for the triangles.

Example 1:

                  Determine the angle of right angled triangle where the measurement of one angle is about 41 degrees.

Solution:

                 Now we calculate the right angle triangle as follows,

                                      x + 41 = 90

                Now subtract the given angle from 90 degree we get,

                                     x = 90 - 41

                                     x = 49

               Thus, the angle of the right triangle is 49 degrees.

 

 

Example 2:

               Determine the angles measurement of a triangle whose sides are a = 7 cm, b = 8 cm and c = 9 cm. Find the angle A and B

Solution:

               Given data: The side measurement is about a = 3cm, b = 4cm and c = 5cm.

               The angles A and B of a triangle are determined as follows,

                              cos A =  `(b^2 + c^2 - a^2)/(2bc)`

                              cos A =  `(8^2 + 9^2 - 7^2)/(2 * 8 * 9)`

                              cos A = `(64 + 81 - 49)/(144)`

                              cos A = `96/144`

                              cos A = 0.666

                              A = cos-1 0.666

                              A = 48.18

               The angle B can be calculated as follows,

                           cos B = `(c^2 + a^2 - b^2)/(2ca)`

                           cos B = `(9^2 + 7^2 - 8^2)/(2 * 9 * 7)`

                           cos B = `(81 + 49 - 64)/(126)`

                           cos B = `66/126`

                           cos B = 0.523

                           B = cos-1 0.523

                           B = 58.41

            Thus, the two angles are determined as A = 48.18 degrees and angle B = 58.41