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Geometry Right Angle

Introduction to geometry right angle:

In geometry, Right angle is nothing but the right angle triangle in which one of the angles is 90 degree. In a right angle, Let x, y and z are the dimensions of the triangle. The right angle triangle is given as,

In geometry, the theorem used to solve right angle triangle is known as pythogoras theorem. In right angle triangle, Pythagoras theorem is given as,

                                                x2 + y2 = z2                        

In right angle triangle, When the addition of two shorter sides of a triangle are squared is equals the square of the longest side or hypotenuse is named as Pythagoras theorem.


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Examples for geometry right angle:


Example1: Find the value of z given that x="4" y = 8?

                        Given: x="4," y="8

                        Solution:

                                    Pythagoras theorem is given as,

                                                x2 + y2 = z2     

                                                42 + 82 = z2                                                       

                                                16 + 64 = z2

                                                80 = z2

                                                Z = sqrt(80)

                                                Z = 8.9

Example2: Find the value of z given that x="9," y = 3?

                        Given: x="9," y="3

                        Solution:

                                    Pythagoras theorem is given as,

                                                x2 + y2 = z2     

                                                92 + 32 = z2                                                       

                                                81 + 9 = z2

                                                90 = z2

                                                Z = sqrt (90)

                                                Z = 9.4

                                                Answer is 9.4

Example3: Given that the hypotenuse is 6, and one side is 4, find the length of the other side?

            Given

                        Let as assume x="4" and z="6

            Solution

                        Pythagoras theorem is given as,

x2 + y2 = z2     

(4)² + y² = (6)²

16 + y² = 64

y² = 64 – 16

y² = 48

y = square root of 48

y = 6.9

                                                 Answer is 6.9


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Additional Examples for geometry right angle:


Example 4: Given that the hypotenuse is 12, and one side is 6, find the length of the other side?

            Given

                        Let as assume y="6" and z="12

            Solution

                        Pythagoras theorem is given as,

x2 + y2 = z2     

(6)² + x² = (12)²

36 + x² = 144

x² = 144 – 36

x² = 108

x = square root of 108

x = 10.39

Answer is 10.39

Example 5: find the value of a given that x="3a," y="4a," z="10?

            Given x="3a," y="4a," z="10

            Solution

                        Pythagoras theorem is given as,

x2 + y2 = z2     

 (3a)² + (4a)² = (10)²

 9a2 + 16a² = 100

 25a² = 100

a² = 100/25

 a² = 4

a= 2

Practice problem:

         Problem1: We are given that x = 3 and y = 4. Add these values to the formula and solve for z?

                                Answer z="5

         Problem2: We are given that x = 5 and z = 13. Add these values to the formula and solve for z?

                                Answer y="12