Answer: a = 31 degrees, 22'
Step-by-step explanation:
From the information given,
x = 10.9
y = 16
z = 30.4
The right triangle formed is shown below
z = 2BC + x
2BC = z - x = 30.4 - 10.9 = 19.5
BC = 19.5/2
BC = 9.75
Considering the right triangle ABC with angle a as the reference angle,
opposite side = BC = 9.75
adjacent side = AB = 16
We would find a by applying the tangent trigonometric ratio which is expressed as
Tanθ = opposite side/adjacent side
tana = 9.75/16
Taking the tan inverse of 9.75/16,
a = tan^-1(9.75/16)
a = 31.36 degrees
We would convert 0.36 degrees to minute
Recall, 1 degree = 60 arcminutes
0.36 degrees = 0.36 * 60 = 21.6 arcminutes
Rounding 21.6 to the nearest minute, it becomes 22
Thus,
a = 31 degrees, 22'