the angle of a triangle are in 3:4:5 then express the smallest angle in centesimal system
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Answer:
Let the angles be (a−d)
0
,a
0
and (a+d)
0
. Then,
a−d+a+a+d=180⇒3a=180⇒a=60.
So, the angles are (60−d)
0
,60
0
and (60+d)
0
.
180
0
=π
c
⇒(60+d)
0
={
180
π
×(60+d)}
c
={
180
(60+d)π
}
c
∴
(60+d)
180
π
(60−d)
=
π
60
⇒
(60+d)
3(60−d)
=1
⇒180−3d=60+d⇒4d=120⇒d=30.
∴ the smallest angle = (60−30)
0
=30
Answered by
0
Let the angles be (a−d)
0
,a
0
and (a+d)
0
. Then,
a−d+a+a+d=180⇒3a=180⇒a=60.
So, the angles are (60−d)
0
,60
0
and (60+d)
0
.
180
0
=π
c
⇒(60+d)
0
={
180
π
×(60+d)}
c
={
180
(60+d)π
}
c
∴
(60+d)
180
π
(60−d)
=
π
60
⇒
(60+d)
3(60−d)
=1
⇒180−3d=60+d⇒4d=120⇒d=30.
∴ the smallest angle = (60−30)
0
=30
0
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