Q. 14.3( 492 Votes )

In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:

(i) Sin A, Cos A

(ii) Sin C, Cos C

Answer :


Given: AB = 24 cm, BC = 7 cm
Pythagoras theorem: the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem for ΔABC, we obtain

AC2 = AB2 + BC2


      = (24)2 + (7)2


      = (576 + 49)


      = 625 cm2


∴ AC =


   AC = 25 cm


As,

To determine when a line is perpendicular and when its a base for a particular angle, first look for the angle for which you are calculating the trigonometric ratio.
The side opposite to which you are calculating angle is called perpendicular, side opposite to right angle is hypotenuse and side left is called base
For example if you have to calculate sin A, then your side opposite to A will be perpendicular and side left other than hypotenuse is base.

(i) Sin A =


      sin A    =


    Cos A =


     cos A   =


(ii) Sin C =


=



Cos C =


=

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