Answer:
See explanation
Step-by-step explanation:
1st photo:
x = [tex]\sqrt{15}[/tex]
[tex]\frac{x}{5} = \frac{3}{x}[/tex]
[tex]x^{2}[/tex] = 15
x = [tex]\sqrt{15}[/tex]
2nd photo:
(a) GEH ~ FGH ~ FEG
similar triangles, use similar corners in the right order
(b) [tex]\frac{FE}{GE} = \frac{GE}{EH}[/tex] AND [tex]\frac{FH}{GH} = \frac{GH}{HE}[/tex]
similar triangles, use similar sides in proportion
3rd photo:
x = 4.5 or 4 1/2
[tex]\frac{x}{3} = \frac{3}{2}[/tex]
2x = 9
x = 4.5 or 4 1/2
4th photo:
Length of string = 118.2 ft
sin(40) = 76/x
x = 76/sin(40) = 118.2
