Respuesta :
Answer:
The change in the angle of elevation is approximately 63.435°
Step-by-step explanation:
The given parameters are;
The speed of the tightrope walker = 3 ft./sec
The altitude at which the tightrope walker is moving = 100 ft.
The horizontal distance of the tightrope walker from the searchlight = 200 feet
The final angle of elevation, θ, is given by the trigonometric ratio as follows;
[tex]tan\angle \theta = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length} = \dfrac{Elevation \ of \, the \ tightrope}{Horizontal \ distance \ to \ the \ tight rope \ walker}[/tex]
[tex]tan\angle \theta = \dfrac{Elevation \ of \, the \ tightrope}{Horizontal \ distance \ to \ the \ tight rope \ walker} = \dfrac{100}{200} = \dfrac{1}{2}[/tex]
[tex]\theta = tan^{-1} \left (\dfrac{1}{2} \right ) \approx 26.565 ^ {\circ}[/tex]
Whereby the tightrope walker was initially vertically overhead the search light, the initial angle of elevation = 90°
The change in the angle of elevation = The initial angle of elevation - The final angle of elevation
Substituting the values gives
The change in the angle of elevation = 90° - 26.565 ≈ 63.435°
Change in the angle of elevation = 63.4°
The original position of the tightrope Walker is vertical
That is, the initial angle of elevation, θ = 90 degrees
Horizontal distance of the Walker = 200 feet
The altitude of the Walker = 100 feet
The final angle of elevation of the tightrope Walker is calculated as follows
[tex]tan \theta \: = \frac{opposite}{adjacent} [/tex]
[tex]tan \: \theta \: = \frac{100}{200} [/tex]
[tex]tan \: \theta \: = 0.5[/tex]
[tex]\theta \: = {tan}^{ - 1} 0.5[/tex]
[tex]\theta = {26.6}^{0} [/tex]
Change in the angle of elevation = Final angle of elevation - Initial angle of elevation
Change in the angle of elevation = 90 - 26.6
Change in the angle of elevation = 63.4°
Learn more here: https://brainly.com/question/19469861
