the angles of a right triangle are in AP. if the greatest angle equals the sum of the         other 2,find the angles.

Asked by derrindarren | 30th Dec, 2015, 09:34: PM

Expert Answer:

Let space straight x comma space straight x plus straight d comma space straight x plus 2 straight d space be space the space angles space of space right space triangle space in space AP.  Sum space of space the space angles space of space the space triangle space is space 180 degree space space therefore straight x plus left parenthesis straight x plus straight d right parenthesis plus left parenthesis straight x plus 2 straight d right parenthesis equals 180 degree therefore 3 straight x plus 3 straight d equals 180 degree straight x plus straight d equals 60 degree............. left parenthesis straight i right parenthesis  The space greatest space angle space equals space the space sum space of space the space other space two space angles therefore straight x plus 2 straight d equals straight x plus left parenthesis straight x plus straight d right parenthesis straight x plus 2 straight d equals 2 straight x plus straight d straight x equals straight d..... left parenthesis ii right parenthesis  From space equation space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space we space get straight x plus straight x equals 60 degree straight x equals 30 degree therefore straight x plus straight d equals straight x plus straight x equals 2 straight x equals 60 degree straight x plus 2 straight d equals straight x plus 2 straight x equals 3 straight x equals 90 degree  Hence space the space three space angles space are space 30 degree comma space 60 degree space and space 90 degree.

Answered by Vijaykumar Wani | 31st Dec, 2015, 10:13: AM