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Mathematics
If the lengths of the sides of a right-angled triangle ABC, right angled at C, are in arithmetic progression, then the value of 5(sin A + sin B) is
Q. If the lengths of the sides of a right-angled triangle
A
BC
,
right angled at
C
,
are in arithmetic progression, then the value of
5
(
s
in
A
+
s
in
B
)
is
135
154
NTA Abhyas
NTA Abhyas 2022
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Answer:
7
Solution:
(
a
+
d
)
2
=
(
a
−
d
)
2
+
a
2
(Pythagoras theorem)
a
2
+
d
2
+
2
a
d
=
a
2
+
d
2
−
2
a
d
+
a
2
⇒
4
a
d
=
a
2
⇒
a
=
4
d
s
in
A
=
a
+
d
a
−
d
=
4
d
+
d
4
d
−
d
=
5
3
s
in
B
=
a
+
d
a
=
5
d
4
d
=
5
4
⇒
5
s
in
A
+
5
s
in
B
=
3
+
4
=
7
⇒
5
(
s
in
A
+
s
in
B
)
=
7