Find the value of each variable.
30 degrees
y
x
60 degrees
20
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Part 1
A.
xequals10 and yequals10 StartRoot 2 EndRoot
B.
xequals20 and yequals20 StartRoot 2 EndRoot
C.
xequals10 and yequals10 StartRoot 3 EndRoot
The correct answer is A.
Given that one angle is 30 degrees and the other angle is 60 degrees in a right triangle, the sides can be found using trigonometric ratios.
For the angle of 30 degrees:
sin(30) = opposite/hypotenuse
sin(30) = y/x
Therefore, y = x * sin(30)
For the angle of 60 degrees:
cos(60) = adjacent/hypotenuse
cos(60) = y/x
Therefore, x = y/cos(60)
Given that x = 20, we can find the value of y:
y = 20 * sin(30)
y = 20 * 1/2
y = 10
Thus, the values of x and y are x=20 and y=10√3, making option A the correct answer.