Question

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 1

i) QR/RP
ii) PR/PQ
iii) QR/PR
iv) PR/RQ

Answer 2

Answer:

• $\rm \sin P=\dfrac{RQ}{PQ}.$
• $\rm \cos Q=\dfrac{RQ}{PQ}.$
• $\rm \tan P=\dfrac{RQ}{PR}.$
• $\rm \tan Q = \dfrac{PR}{RQ}.$

Step-by-step explanation:

In a right-angled triangle,  

The sine of an angle is equal to the ratio of the perpendicular to the hypotenuse of the triangle.

The cosine of an angle is equal to the ratio of the base to the hypotenuse of the triangle.

The tangent of an angle is equal to the ratio of perpendicular to the base of the triangle.

For an angle in a right-angled triangle, the perpendicular is that side of the triangle which is opposite to that angle, the base is that side which is adjacent to that angle and the hypotenuse is the largest side of the triangle.

Thus,

$\rm \sin P=\dfrac{RQ}{PQ}.\\\cos Q=\dfrac{RQ}{PQ}.\\\tan P=\dfrac{RQ}{PR}.\\\tan Q = \dfrac{PR}{RQ}.$