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° = ∅[tex]_{1}[/tex] + ∅[tex]_{2}[/tex].................................(1)
From the triangle KGI,
Trignometric ratio,
tan ∅[tex]_{1}[/tex] = [tex]\frac{Opp}{Adj}[/tex].................................(2)
Where, Opp = 9
Adj = 12
Equation (2) becomes,
tan ∅[tex]_{1}[/tex] = [tex]\frac{9}{12}[/tex]
= 0.75
∅[tex]_{1}[/tex] = [tex]tan^{-1}[/tex] 0.75
∅[tex]_{1}[/tex] = 36.87°
From the equation (1),
∅[tex]_{2}[/tex] = 90° - ∅[tex]_{1}[/tex]
= 90° - 36.87°
∅[tex]_{2}[/tex] = 53.13°
From the triangle IGM,
tan ∅[tex]_{2}[/tex] = [tex]\frac{Opp}{Adj}[/tex]..........................(3)
Where, Opp = GM
Adj = 12
∅[tex]_{2}[/tex] = 53.13°
Equation (2) becomes,
tan 53.13° = [tex]\frac{GM}{12}[/tex]
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.
