In ∆ABC,<c is a right angle. 'a' and 'b' are the legs and 'c' is the hypotenuse.Find the third side if: a=5,c=13
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We have ,
∠A+∠B+∠C=180
∘
⇒30
∘
+∠B+90
∘
=180
∘
[∵∠A=30
∘
and∠C=90
∘
]
⇒∠B=180
∘
−120
∘
=60
∘
Now , cosA=
AB
AC
⇒cos30
∘
=
40
AC
⇒
2
3
=
40
AC
⇒AC=
2
3
×40⇒AC=20
3
units
and , sinA=
AB
BC
⇒sin30
∘
=
40
BC
⇒
2
1
=
40
BC
⇒=40×
2
1
=20 units
Hence AC = 20
3
units , BC=20 units and ∠B=60
∘
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