The shortest possible length of the ladder if the top of it is 23 feet off the ground is 24 ft.
"It is a triangle in which one of the angle measures 90° "
"It is the longest side in the right triangle."
"In right triangle, a² + b² = c², where c is hypotenuse and a, b are other two sides of the right triangle."
"In right triangle for angle x, [tex]sin(x)=\frac{opposite~ side~ of~ angle~x}{hypotenuse}[/tex] "
For given question,
Consider the following figure.
In right triangle WXY, WX is 23 feet as a window screen is 23 feet above the ground.
WY represents the ladder.
that is the hypotenuse of right triangle WXY is the length of the ladder.
A ladder leans against a building and forms a 75 degree angle with the ground
⇒ ∠WYX = 75°
Consider the sine of ∠WYX .
[tex]\Rightarrow sin(75)=\frac{WX}{WY}\\\\ \Rightarrow 0.9659=\frac{23}{WY}\\\\ \Rightarrow WY=\frac{23}{0.9659}\\\\ \Rightarrow WY=23.81\\\\\Rightarrow WY\approx 24[/tex]
This means the hypotenuse WY is approximately 24 ft.
Therefore, the shortest possible length of the ladder if the top of it is 23 feet off the ground is 24 ft.
Learn more about the hypotenuse here:
https://brainly.com/question/8587612
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