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IN A TRIANGLE THE LENGTH OF A LARGER SIDES ARE 9 AND10. IF THE ANGLE ARE IN AP, THE LENGTH OF THE THIRD SIDE CAN BE?

IN A TRIANGLE THE LENGTH OF A LARGER SIDES ARE 9 AND10. IF THE ANGLE ARE IN AP, THE LENGTH OF THE THIRD SIDE CAN BE?
 

Grade:11

1 Answers

ANIRUDH GHILDIYAL
21 Points
5 years ago
Let the angles be a-d, a, a+d.
sum of all angles is equal to 180 degrees.
a-d + a + a+d = 180
3a = 180, a= 60 degrees.
Using sin formula sin A/a= sin B/b = sin C/c
We get sin a/9 = sin(a+d) /10
sin 60/9 = sin (60+d)/10, on solving we get d = 14.2
Using sin formula again and let third side be x we get
sin 60/9 = sin(60-14.2)/x on solving we get x = 7.45 cm
Answer 7.45 cm

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