contestada

A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 ft on the wall. Find to the nearest degree the angle the ladder makes with the wall.

Respuesta :

calculista

Answer:

The angle the ladder makes with the wall is equal to [tex]22\°[/tex]

Step-by-step explanation:

Let

x-------> the angle the ladder makes with the wall

see the attached figure to better understand the problem

we know that

In the right triangle ABC

[tex]tan(x)=\frac{AB}{BC}[/tex]

we have

[tex]AB=6\ ft[/tex]

[tex]BC=15\ ft[/tex]

substitute

[tex]tan(x)=\frac{6}{15}[/tex]

[tex]x=arctan(\frac{6}{15})=22\°[/tex]

Ver imagen calculista
  • The angle the ladder makes with the wall is 22º

To solve this question, we would employ the principle of Pythagoras theorem.

The foot of the ladder from the wall being the opposite side, while the height of the ladder being the adjacent side. We are asked to find the angle the ladder makes with the wall.

In a Pythagoras triangle, we know that Tan θ = [tex]\frac{opp}{adj}[/tex], this also means that

Tan θ = 6/15

Tan θ = 0.4

θ = Tan⁻¹ (0.4)

θ = 21.8º

Since we are asked to approximate to the nearest angle, we have 22º.

For more on pythagoras triangles, see https://brainly.com/question/15540177

Otras preguntas