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9. A ladder of length 23 feet leans against the side of a building. The angle of elevation of the ladder is 76. Find the distance from the top of the ladder to the ground. Round your answer to two decimals.
A)
5.73 feet
B)
22.32 feet
C)
5.56 feet
D)
18.96 feet
E)
13.02 feet

Respuesta :

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Answer:

  • B) 22.32 feet

[tex] \quad\rule{300pt}{1pt}[/tex]

Solution:

we are given that , a ladder is placed against a side of building , which forms a right angled triangle . We wre given one side of a right angled triangle ( hypotenuse ) as 23 feet and the angle of elevation as 76 ° . We can find the Perpendicular distance from the top of the ladder go to the ground by using the trigonometric identity:

[tex] \qquad\quad\bull ~{\boxed{\bf{ Sin\theta =\dfrac{Perpendicular}{Hypotenuse}}} }~\bull[/tex]

Here,

  • hypotenuse = 23 feet
  • [tex]\theta [/tex] = 76°
  • Value of Sin[tex]\theta [/tex] = 0.97
  • Perpendicular = ?

[tex] \quad\dashrightarrow\quad \sf { sin\theta =\dfrac{P}{H}}[/tex]

[tex] \quad\dashrightarrow\quad \sf { sin76° =\dfrac{P}{23}}[/tex]

[tex] \quad\dashrightarrow\quad \sf { 0.97=\dfrac{P}{23}}[/tex]

[tex] \quad\dashrightarrow\quad \sf {P = 0.97 \times 23 }[/tex]

[tex] \quad\dashrightarrow\quad \sf { P = 22.32}[/tex]

‎ㅤ‎ㅤ‎ㅤ~Hence, the distance from the top of the ladder to the ground is 22.32 feet !

[tex] \rule{300pt}{2pt}[/tex]

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