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

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,