Q. 13.7( 33 Votes )

In the Fig. 8.12, R is the right angle of ΔPQR. Write the following ratios.

(i) sin P (ii) cos Q

(iii) tan P (iv) tan Q


Answer :

For any right-angled triangle,

sinθ = Opposite side Side/Hypotenuse


cosθ = Adjacent sideSide/Hypotenuse


tanθ = sinθ/cosθ


= Opposite side Side/Adjacent sideSide


cotθ = 1/tanθ


= Adjacent sideSide/Opposite side Side


secθ = 1/cosθ


= Hypotenuse/Adjacent sideSide


cosecθ = 1/sinθ


= Hypotenuse/Opposite side Side


In the given triangle let us understand, the Opposite side and Adjacent sidesides.


So for P,


Opposite side Side = QR


Adjacent sideSide = PR


So, for Q,


Opposite side Side = PR


Adjacent sideSide = QR


In general for the side Opposite side to the 90° angle is the hypotenuse.


So, for Δ PQR, hypotenuse = PQ


(i) sin P = Opposite side Side/Hypotenuse


= QR/PQ


(ii) cos Q = Adjacent sideSide/Hypotenuse


= QR/PQ


(iii) tan P = sinθ/cosθ


= Opposite side Side/Adjacent sideSide


= QR/PR


(iv) tan Q = sinθ/cosθ


= Opposite side Side/Adjacent sideSide


= PR/QR


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