Question

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

Answer 1

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.

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)` =
`(Opp)/(Adj)`.................................(2)

Where, Opp = 9

Adj = 12

Equation (2) becomes,

tan ∅
`_(1)` =
`(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)` =
`(Opp)/(Adj)`..........................(3)

Where, Opp = GM

Adj = 12

∅
`_(2)` = 53.13°

Equation (2) becomes,

tan 53.13° =
`(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.