Mathematics, 17.04.2020 18:35 iisofieii1978

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

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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° = ∅ $_{1}$ + ∅ $_{2}$ .................................(1)

From the triangle KGI,

Trignometric ratio,

tan ∅ $_{1}$ = $\frac{Opp}{Adj}$ .................................(2)

Where, Opp = 9

Adj = 12

Equation (2) becomes,

tan ∅ $_{1}$ = $\frac{9}{12}$

= 0.75

∅ $_{1}$ = $tan^{-1}$ 0.75

∅ $_{1}$ = 36.87°

From the equation (1),

∅ $_{2}$ = 90° - ∅ $_{1}$

= 90° - 36.87°

∅ $_{2}$ = 53.13°

From the triangle IGM,

tan ∅ $_{2}$ = $\frac{Opp}{Adj}$ ..........................(3)

Where, Opp = GM

Adj = 12

∅ $_{2}$ = 53.13°

Equation (2) becomes,

tan 53.13° = $\frac{GM}{12}$

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.

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

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

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