The question is an illustration of trigonometry ratio, and the tangent of the angle is 12/13
How to determine the tangent of the angle?
Let the angle be x.
The sine of the angle is given as:
sin(x) = 5/13
The sine of an angle is calculated using:
sin(x) = opposite/hypotenuse
By Pythagoras theorem, we have:
Hypotenuse^2 = Adjacent^2 +Opposite^2
This gives
13^2 = Adjacent^2 + 5^2
Rewrite as:
Adjacent^2 = 13^2 - 5^2
Evaluate
Adjacent^2 = 144
Take the square root of both sides
Adjacent = 12
The tangent is then calculated using
tan(x) = Adjacent/Hypotenuse
So, we have:
tan(x) = 12/13
Hence, the tangent of the angle is 12/13
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