Answer: [tex]32.36\ ft[/tex]
Step-by-step explanation:
Given
Ladder is leaned and make an angle of [tex]68^{\circ}[/tex]
Electric box is 30 ft up the ground.
Suppose x is the length of ladder
From the figure, we can write
[tex]\Rightarrow \sin 68^{\circ}=\dfrac{30}{x}\\\\\Rightarrow x=\dfrac{30}{\sin 68^{\circ}}\\\\\Rightarrow x=32.36\ ft[/tex]
The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The length of the ladder is 32.356 feet.
The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
As it is given that the height of the electric box from the bottom is 30 feet, while the ladder makes an angle of 68° with the ground.
The length of the ladder can be found using the trigonometric functions, therefore, the length of the ladder can be written as,
[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\\\Sine(\angle C) = \dfrac{AB}{\text{Length of the ladder}}\\\\\\{\text{Length of the ladder}}= \dfrac{AB}{Sine(\angle C) }\\\\\\{\text{Length of the ladder}}= \dfrac{30}{Sine(68^o) }\\\\\\{\text{Length of the ladder}}= 32.356\ feet[/tex]
Hence, the length of the ladder is 32.356 feet.
Learn more about Sine:
https://brainly.com/question/21286835
