86.5k views
21 votes
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?​

2 Answers

10 votes

Answer:

0.75 feet

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
User Nathiel Barros
by
6.3k points
6 votes

Answer:

0.748 ft (nearest thousandth)

Explanation:

Use the tan trig ratio:


\tan(\theta)=(O)/(A)

where:


  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

Given:


  • \theta = 14°
  • O = x
  • A = 3 ft


\implies \tan(14)=(x)/(3)


\implies x=3\tan(14)


\implies x=0.7479840085...

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

User Nabil El
by
6.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.