Answer:
37.98°
Explanation:
You want the value of θ in a right triangle with a hypotenuse of 13 cm and a side opposite the angle of 8 cm.
Sine
The sine relation is ...
Sin = Opposite/Hypotenuse
In this figure, that means ...
sin(θ°) = (8 cm)/(13 cm)
The value of θ is found using the arcsin function:
θ° = arcsin(8/13) ≈ 37.98°
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Additional comment
You will note the calculator mode is set to DEGrees.
The inverse function of the sine function is called the "arcsine" function. It is represented on most calculator keypads using a -1 exponent. (-1 is usually used with a function name to signify the inverse function. Here, the inverse sine function gives "the angle whose sine is ...".)
Typical units used for angles are degrees, radians, and gradians. The number that is the argument of the inverse sine function is a "pure number" with no units. If you find your calculation causes it to have units, then you need to check your work. (Here the units of cm in numerator and denominator cancel, leaving the unitless value 8/13.)