If the ratio of the sine of an acute angle to its cosine is 5: 12, then what will the value of sine of that angle be?

The ratio of the sine of an acute angle to its cosine  = 5 : 12

Formula used:  

h² = (p² + b²)​

The ratio of the sine of an acute angle to its cosine 5 : 12

Where h = hypotenuse, b = base and p = perpendicular

sinθ = $$\frac{p}h$$​

cosθ = $$\frac{b}h$$​

=> $$\frac{p}h : \frac{b}h$$​ = 5 : 12

=> $$\frac{p}b = \frac{5}{12}$$​

Now,

By Pythagoras theorem,

h² = (p² + b²)

=> h² = (5² + 12²)

=> h² = (25 + 144)

=> h² = 169

=> h = 13 

Now,

Therefore, the value of sine = $$\frac{p}h$$​= $$\bf \frac{5}{13}.$$​