In the diagram below of right triangle KMI, altitude IG is drawn to hypotenuse KM.
If KG = 9 and IG= 12, the length of GM is

The length of GM is 16. It is obtained from the right triangle KMI, altitude IG is drawn to hypotenuse KM and KG = 9 and IG= 12.

Step-by-step explanation:

The given is,

                  Right triangle KMI

                  KG = 9

                  IG= 12

Step:1

                From the triangle KMI,

                           90° = ∅ + ∅.................................(1)

                From the triangle KGI,

                Trignometric ratio,

                          tan ∅ = .................................(2)

                Where, Opp = 9

                               Adj = 12

               Equation (2) becomes,

                          tan ∅ =

                                     = 0.75

                                 ∅ = 0.75

                                 ∅ = 36.87°

              From the equation (1),

                                 ∅ =  90° - ∅

                                      = 90° - 36.87°

                                ∅ = 53.13°

             From the triangle IGM,

                           tan ∅ = ..........................(3)

              Where, Opp = GM

                             Adj = 12

                               ∅ = 53.13°

             Equation (2) becomes,

                   tan 53.13° =

                             GM = (1.333)(12)

                                    = 15.999

                             GM ≅ 16

Result:

            The length of GM is 16. It is obtained from the right triangle KMI, altitude IG is drawn to hypotenuse KM and KG = 9 and IG= 12.

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8

step-by-step explanation:

this is a subtraction problem.

10 - 2 = 8