Answer:
x = [tex]24^{o}[/tex]
Step-by-step explanation:
r + s = 70 feet
Applying Pythagoras theorem to the triangle formed by cable r;
[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]
[tex]/r/^{2}[/tex] = [tex]/20/^{2}[/tex] + [tex]/8/^{2}[/tex]
[tex]r^{2}[/tex] = 400 + 64
= 464
r = [tex]\sqrt{464}[/tex]
= 21.541
Length of cable r is 21.54 feet.
So that,
r + s = 70 feet
21.54 feet + s = 70 feet
s = 70 feet - 21.54 feet
= 48.46 feet
Length of cable s is 48.46 feet.
Applying trigonometric function to the triangle formed by cable s, we have;
Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin x = [tex]\frac{20}{48.46}[/tex]
= 0.4127
x = [tex]Sin^{-1}[/tex] 0.4127
= 24.3746
x = [tex]24^{o}[/tex]
The measure of angle that s makes with the ground is approximately [tex]24^{o}[/tex].
