Maryalhussein6
contestada

1) Aladder is placed against the wall of a building such that the bottom of the ladder is 3 ft from the bottom of the wall. If the ladder forms a 14 degree angle with the building, how high up the wall does the ladder reach?​

Respuesta :

Answer:

0.75 feet

Step-by-step explanation:

Let's picture a right triangle, where :

  • AB = distance b/w bottom of ladder and bottom of wall = 3 feet
  • AC = length of ladder [what we need to find!]
  • BC = distance b/w top of building and bottom of ladder

Let the height of the ladder be x.

  • Then, taking the ratio b/w the adjacent and opposite sides...
  • ⇒ tan 14° = 0.249
  • ⇒ tan 14° = x/3
  • ⇒ x/3 = 0.249
  • ⇒ x = 0.249 x 3
  • ⇒ x = 0.747 ≅ 0.75 feet
semsee45

Answer:

0.748 ft (nearest thousandth)

Step-by-step explanation:

Use the tan trig ratio:

[tex]\tan(\theta)=\dfrac{O}{A}[/tex]

where:

  • [tex]\theta[/tex] is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

Given:

  • [tex]\theta[/tex] = 14°
  • O = x
  • A = 3 ft

[tex]\implies \tan(14)=\dfrac{x}{3}[/tex]

[tex]\implies x=3\tan(14)[/tex]

[tex]\implies x=0.7479840085...[/tex]

Therefore, the ladder reaches up the wall 0.748 ft (nearest thousandth)

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