Answer:
1)7.288 feet
2)11.6 feet
3)safe
4) 3.7 feet
5) ∅[tex]= tan^{-1}(1.5) = 56.31 degrees[/tex]
6)∅1[tex]= tan^{-1}(2) = 63.43 degrees[/tex]
∅2[tex]= tan^{-1}(1.2) = 50.19 degrees[/tex]
Step-by-step explanation:
1) The door barn is rectangular in shape. The length is 9 feet and The angle between diagonal and side is 39 degrees.
Applying trigonometry,
tan(39) = [tex]\frac{opposite}{adjacent} = \frac{s}{9}[/tex] = 0.809
Thus, s= [tex](9)(0.809) = 7.288 feet[/tex]
2) Applying pythagoras theorm,
[tex](Diagonal)^{2} = (9)^{2} + (7.288)^{2} =134.115[/tex]
Diagonal length (d) = 11.58 feet. Nearest tenth place = 11.6 feet
3) The length of ladder is 14 foot and height from ground is 13.5 feet.
Applying trigonometry,
sin(∅) = [tex]\frac{opposite}{hypotenous} = \frac{13.5}{14}[/tex] = 0.964
∅ = angle of elevation = [tex]sin^{-1}(0.964)[/tex] = 74.57 ≈ 75 degrees.
Thus tractor can climb safely.
4)Applying, pythgoras theorm,
[tex]14^{2} = (13.5)^{2} + x^{2}[/tex]
x = [tex]\sqrt{14^{2}-(13.5)^{2}} = 3.708[/tex]
Thus, ladder should be placed at distance 3.7 feet
5)Let angle of elevation be ∅.
tan(∅) = [tex]\frac{30}{20} = 1.5[/tex]
∅[tex]= tan^{-1}(1.5) = 56.31 degrees[/tex]
6)After moving 5 feet closer to barn, Let angle of elevation for light near barn be ∅1 and for farther one be ∅2.
Thus,
tan(∅1) = [tex]\frac{30}{15} = 2[/tex]
∅1[tex]= tan^{-1}(2) = 63.43 degrees[/tex]
tan(∅2) = [tex]\frac{30}{25} = 1.2[/tex]
∅2[tex]= tan^{-1}(1.2) = 50.19 degrees[/tex]
