Question

In the adjoining figure, `∠B  = 90° , ∠BAC = theta° , BC = CD = 4cm and AD = 10 cm`. find  (i)  sin theta and (ii) `costheta`

Answer 1

In ΔABD,
Using Pythagoras theorem, we get

AB= `sqrt(AD^2-BD^2)`

= `sqrt(10^2-8^2)`

=`sqrt(100-64)`

=`sqrt(36)`

=6cm

Again,
In ΔABC,
Using Pythagoras therem, we get

AC= `sqrt(AB^2 +BC^2)`

=`sqrt(6^2+4^2)`

=`sqrt(36+16)`

=`sqrt(52)`

=2`sqrt(13)`cm

Now, 

(i) `sintheta = (BC)/(AC)`

   =`4/(2sqrt(13))`

  =`2/sqrt(13)`

  =`(2 sqrt(13))/13`

(ii) `cos theta = (AB)/(AC)`

  = `6/(2sqrt(13))`

  =`3/sqrt(13)`

  =`(3sqrt(13))/13`