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PLEASE HELP ME MEDAL AND FANS AWARDED.. The top of a ladder is 10 meters from the ground when the ladder leans against the wall at an angle of 35.5° with respect to the ground. If the ladder is moved by x meters toward the wall, it makes an angle of 54.5° with the ground, and its top is 14 meters above the ground. What is x rounded to the nearest meter?

Respuesta :

For this specific problem, x rounded to the nearest meter is 4. I am hoping that this answer has satisfied your query about and it will be able to help you, and if you’d like, feel free to ask another question.

lublana

Answer:

The value of x=4 meters.

Step-by-step explanation:

Let DC=x m

In triangle ABC

[tex]\theta=35.5{\circ}[/tex]

AB=10 m

We know that

[tex]tan\theta=\frac{perpendicular side }{Base}[/tex]

[tex]tan35.5^{\circ}=\frac{AB}{BC}[/tex]

[tex]0.713=\frac{10}{BC}[/tex]

[tex]BC=\frac{10}{0.713}[/tex]

BC=14.02m

In triangle EBD

EB=14 m

[tex]\theta=54.5^{\circ}[/tex]

[tex]tan54.5=\frac{EB}{BD}[/tex]

[tex]1.4019=\frac{14}{BD}[/tex]

[tex]BD=\frac{14}{1.4019}[/tex]

BD=9.98 m.

BC=BD+DC

14.02=9.98+x

By using substituting property

x=14.02-9.98

By using subtraction property of equality

x=4.04

x=4 ( nearest meter)

The value of x=4 m.

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