Q. 5 B5.0( 2 Votes )

Find the value of the following : (a) sin θ (b) cos θ (c) tan θ from the figures given below :


Answer :

Firstly, we have to find the value of XM and we can find out with the help of Pythagoras theorem


So, In ∆XMZ


(XM)2 + (MZ)2 = (XZ)2


(XM)2 + (16)2 = (20)2


(XM)2 = (20)2 – (16)2


Using the identity a2 –b2 = (a+b) (a – b)


(XM)2 = (20–16)(20+16)


(XM)2 = (4)(36)


(XM)2 = 144


XM =144


XM =±12


But side XM can’t be negative. So, XM = 12


Now, In ∆XMY we have the value of XM and MY but we don’t have the value of XY.


So, again we apply the Pythagoras theorem in ∆XMY


(XM)2 + (MY)2 = (XY)2


(12)2 + (5)2 = (XY)2


144 + 25 = (XY)2


(XY)2 = 169


XY =169


XY =±13


But side XY can’t be negative. So, XY = 13


a. sin θ


We know that,



In ∆XMY


Side opposite to θ = MY = 5


Hypotenuse = XY = 13


So,


b. cos θ


We know that,




In ∆XMY


Side adjacent to θ = XM = 12


Hypotenuse = XY = 13


So


c. tan θ


We know that,




In ∆XMY


The side opposite to θ = MY = 5


Side adjacent to θ = XM = 12


So,


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