Respuesta :
Answer:
A) 47.17
B) 10.2 feet
Step-by-step explanation:
dont forget to switch the calculator to degrees when doing this
For A)
arcsin(11/15)=angle of elevation
47.17=angle of elevation
For B)
tan(47.17)=11/x
11/tan(47.17)=x
10.2=x
read comments for other stuff that i forgot to put in here
Angle of elevation is equals to 47.14 degrees and distance from the base of the house is equals to [tex]2\sqrt{26} foot[/tex].
What is angle of elevation?
" Angle of elevation is defined as the angle between horizontal plane and the observation line of sight."
Formula used
[tex]sin\alpha = \frac{opposite side}{hypotenuse}[/tex]
Pythagoras theorem
[tex](Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}[/tex]
According to the question,
Length of the ladder ' hypotenuse'= 15 foot
Height to reach a point ' perpendicular' = 11feet
'[tex]\alpha[/tex]' represents the angle of elevation
[tex]'x'[/tex] represents the base of the house
Substitute the value to get the value of angle of elevation we have,
[tex]sin\alpha = \frac{11}{15}[/tex]
⇒ [tex]\alpha = sin^{-1} (0.7333)[/tex]
⇒[tex]\alpha = 47.14[/tex] degrees
Substitute the value in the formula to get the value of base we have,
[tex](15)^{2}= (11)^{2} +x^{2}[/tex]
⇒[tex]x^{2} = 225 - 121[/tex]
⇒[tex]x^{2} = 104[/tex]
⇒[tex]x=\sqrt{104}[/tex]
⇒[tex]x= 2\sqrt{26}[/tex] foot
Hence, angle of elevation is equals to 47.14 degrees and distance from the base of the house is equals to [tex]2\sqrt{26} foot[/tex].
Learn more about angle of elevation here
https://brainly.com/question/21137209
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