Question

# In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios. (i) (ii) (iii) tan θ = 11 (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii)

Solution

## (i) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Perpendicular side = 2 and Hypotenuse = 3 Therefore, by Pythagoras theorem, Now we substitute the value of perpendicular side (BC) and hypotenuse (AC) and get the base side (AB) Therefore, Hence, Base = Now, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (ii) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Base = 4 and Hypotenuse = 5 Therefore, By Pythagoras theorem, Now we substitute the value of base side (AB) and hypotenuse (AC) and get the perpendicular side (BC) Hence, Perpendicular side = 3 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (iii) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Base = 1 and Perpendicular side = 5 Therefore, By Pythagoras theorem, Now we substitute the value of base side (AB) and the perpendicular side (BC) and get hypotenuse (AC) Hence, Hypotenuse = Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (iv) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Perpendicular side = 11 and Hypotenuse = 15 Therefore, By Pythagoras theorem, Now we substitute the value of perpendicular side (BC) and hypotenuse(AC) and get the base side (AB) Hence, Base = Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (v) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Base = 12 and Perpendicular side = 5 Therefore, By Pythagoras theorem, Now we substitute the value of base side (AB) and the perpendicular side (BC) and get hypotenuse (AC) Hence, Hypotenuse = 13 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (vi) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Perpendicular side = and Hypotenuse = 2 Therefore, By Pythagoras theorem, Now we substitute the value of perpendicular side (BC) and hypotenuse(AC) and get the base side (AB) Hence, Base = 1 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (vii) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Base = 7 and Hypotenuse = 25 Therefore, By Pythagoras theorem, Now we substitute the value of base side (AB) and hypotenuse (AC) and get the perpendicular side (BC) Hence, Perpendicular side = 24 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (viii) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Base = 15 and Perpendicular side = 8 Therefore, By Pythagoras theorem, Now we substitute the value of base side (AB) and the perpendicular side (BC) and get hypotenuse (AC) Hence, Hypotenuse = 17 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (ix) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Base = 12 and Perpendicular side = 5 Therefore, By Pythagoras theorem, Now we substitute the value of base side (AB) and the perpendicular side (BC) and get hypotenuse (AC) Hence, Hypotenuse = 13 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (x) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Base = 5 and Hypotenuse = 13 Therefore, By Pythagoras theorem, Now we substitute the value of base side (AB) and hypotenuse (AC) and get the perpendicular side (BC) Hence, Perpendicular side = 12 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, (xi) Given: …… (1) By definition, …... (2) By Comparing (1) and (2) We get, Perpendicular side = 1 and Hypotenuse = Therefore, By Pythagoras theorem, Now we substitute the value of perpendicular side (BC) and hypotenuse (AC) and get the base side (AB) Hence, Base side = 3 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore,   (xii) Given: ……(1) By definition, …... (2) By Comparing (1) and (2) We get, Base = 12 and Hypotenuse = 15 Therefore, By Pythagoras theorem, Now we substitute the value of base side (AB) and hypotenuse (AC) and get the perpendicular side (BC) Hence, Perpendicular side = 9 Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, Now, Therefore, MathematicsRD Sharma (2014)Standard X

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