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in Trigonometry by (71.9k points)
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In `DeltaABC,angleB=90^(@)` , if `AB=5cm, BC=12` cm , then find the vlaues of the following :
(a) Sin A
(b) Cos A
cot A
cosec C
( e) sec C
tan C

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In `DeltaABC` , from Pythagoras theorem
`AC^(2)=AB^(2)+BC^(2)=5^(2)+12^(2) =25 +144=169`
`rArr AC=13`cm
For `angle` A, base is AB , perpendicular is BC.
For `angle` base is BC , perpendicular is AB,
while hypotenuse is same i.e., AC for both the angles
(a) `sin A =("Perpendicular")/("hypotenuse")=(BC)/(AC)=(12)/(13)`
(b)`cos A =(" base")/("hypotenuse")=(AB)/(AC)=(5)/(13)`
(c ) `cot A =(" base")/("perpendicular")=(AB)/(BC)=(5)/(12)`
(d) `"cosec" C=(" hypotenuse")/("perpendicular")=(AC)/(AB)=(13)/(5)`
(e ) `sec C=(" hypotenuse")/("base")=(AC)/(BC)=(13)/(12)`
(f) `tan C=(" perpendicular")/("base")=(AB)/(BC)=(5)/(12)`
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