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Answer:
8a. x = 16√3
8b. y = 8√3
Step-by-step explanation:
8a. Determination of the value of x
Adjacent = 24
Hypothenus = x
Angle θ = 30°
The value of x can be obtained by using cosine ratio as illustrated below:
Cos θ = Adjacent /Hypothenus
Cos 30 = 24 / x
√3/2 = 24/x
Cross multiply
x × √3 = 2× 24
x × √3 = 48
Divide both side by √3
x = 48/√3
Rationalise
x = 48/√3 × √3/√3
x = 48√3 / √3 × √3
x = 48√3 / 3
x = 16√3
8b. Determination of the value of y
Opposite = y
Adjacent = 24
Angle θ = 30°
The value of y can be obtained by using Tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 30 = y / 24
1 / √3 = y /24
Cross multiply
y × √3 = 1 × 24
y × √3 = 24
Divide both side by √3
y = 24 /√3
Rationalise
y = 24 /√3 × √3/√3
y = 24 ×√3 / √3 × √3
y = 24√3 / 3
y = 8√3
Part 1:
The statement that is true about <span>the line passing through points A and B is
</span><span>The line has infinitely many points.
</span>
<span>Beacause of the arrows at the endpoints, the line does not have a finite length that can be measured.
</span><span><span>Any segment with at least two points has infinitely many points, because, intuitively, given any two distinct points, there is a third one, distinct from both of them, say, the middle point.
Thus, t</span>here are not only two points on the entire line.
The line can be called AB or BA, so there is not only one way to name the line.
</span>
Part 2:
Line FM can also be named line MF.
Therefore, the correct name for line FM is line MF.