What is the value of cos C in the given right angled triangle ABC? * Captionless Image
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Answer:
ΔABC is right angled at B, so AC is the hypotenuse.
AC−AB=1 ...Given ....(1)
By Pythagoras theorem,
AC
2
=AB
2
+BC
2
BC
2
=AC
2
−AB
2
7
2
=(AC−AB)(AC+AB)
49=1(AC+AB)
So, AC+AB=49 ....(2)
Adding (1) and (2) we get,
⇒2AC=50
⇒AC=25 cm
Sbstitute in eq (2), we get
AB=24 cm.
Now, cosA+sinA=
AC
AB
+
AC
BC
=
25
24
+
25
7
=
25
31
⇒cosA+sinA=
25
31
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