Answer:
a. 53°, 307°
Step-by-step explanation:
Okay, let's work through this step-by-step:
1) We are given that sin(A) = 0.8.
2) To find the values of A that satisfy this equation, we need to take the inverse sine (arcsin) of 0.8.
3) The inverse sine function gives us two possible angles:
arcsin(0.8) ≈ 53.13° and 180° - 53.13° = 126.87°
4) Therefore, the values of A that make the statement true are:
a) 53° and 307°
This is the correct answer, as 53° and 307° are the only options provided that satisfy the given condition of sin(A) = 0.8.
The other options are incorrect:
b) 37° and 143° do not have a sine value of 0.8.
c) 539° and 1270° are not valid angle values.
d) 53° and 233° do not have a sine value of 0.8.