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The recommended angle for a ladder relative to the ground is 75 degrees or greater. If a 17 foot ladder is leaning against a building with the base of the ladder 4 feet from the wall. What angle does the ladder make with the ground? Express your answer using degree measure rounded to one decimal place.

Respuesta :

Answer:

[tex]\theta = 76.4 degree[/tex]

Explanation:

The distance of the foot of the ladder is 4 feet from the wall

length of the ladder is given as 17 foot

so we will have

[tex]cos\theta = \frac{base}{hypotaneuse}[/tex]

so here we have

base = 4 ft

hypotenuse = 17 ft

now we have

[tex]cos\theta = \frac{4}{17}[/tex]

[tex]\theta = cos^{-1} \frac{4}{17}[/tex]

[tex]\theta = 76.4 degree[/tex]

Answer:

76.4°

Explanation:

Length of ladder, L = 17 foot

Distance of ladder from the wall, d = 4 feet

Let θ be the angle which makes ladder with the horizontal ground.

According to the diagram

[tex]Cos \theta  = \frac{d}{L}[/tex]

By substituting the values, we get

[tex]Cos \theta  = \frac{4}{17}[/tex]

[tex]Cos \theta  = 0.2353[/tex]

θ = 76.4°

Thus, the ladder makes an angle 76.4° with the ground.

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