Question

Given GKH with KG = 15, HK = 13,GH = 14. Let KM = 12 be the altitude. If HM = 5, which is
the largest acute angle?

Answer 1

Given : KG = 15, HK = 13,GH = 14.

 KM = 12 be the altitude.  

HM =  5

To Find :  which is the largest acute angle

Solution:

KG = 15, HK = 13,GH = 14.

13²  + 14² > 15²  hence its an acute angles triangle

Largest acute angle will be opposite side  KG = 15  Hence angle H

HM = 4  , KM = 12   and HK = 13 is a right angles triangles

Hence  Sin H  =  12/13

=> H = Sin⁻¹(12/13)    or   Cos⁻¹(5/13)   or Tan⁻¹(12/5)  

=> H = 67.38°

and H is the largest angle

Largest acute angle is  67.38°

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