Answer:
71°
Step-by-step explanation:
The sine of an angle is equal to the cosine of its complement. This relation can be used to find the value of x.
Setup
Using the relation between sine and cosine, we have ...
sin(x) = cos(90° -x) = cos(19°)
Solution
Equating the arguments of the cosine function, we have ...
90° -x = 19°
x = 71° . . . . . . . add x-19° to both sides of the equation
The value of x is 71°.
Alternate solution
A calculator can be used to find the value of x:
sin(x) = cos(19°)
Using the inverse sine function to find the angle, given its sine value:
x = arcsin(cos(19°))
x = 71°
