If θ is an acute angle and cos θ = 39/89 what is the value of sinθ?

Given: $$\cos \theta = \frac{39}{89}$$​​

Formula Used: $$\sin^2 \theta = 1 - \cos^2 \theta$$​​

Substituting the value of $$\cos \theta$$​into the identity:

​$$\sin^2 \theta + \left(\frac{39}{89}\right)^2 = 1$$​​

​$$\sin^2 \theta + \frac{1521}{7921} = 1$$​​

​$$\sin^2 \theta = 1 - \frac{1521}{7921}$$​​

​$$\sin^2 \theta = \frac{6400}{7921} ​$$  

​$$\sin \theta = \sqrt{\frac{6400}{7921}} = \frac{80}{89} ​$$​​

$$\sin \theta = \frac{80}{89}.$$​​

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