Question

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?

Answer 1

Answer:

The value of x=4 meters.

Step-by-step explanation:

Let DC=x m

In triangle ABC

$\theta=35.5{\circ}$

AB=10 m

We know that

$tan\theta=\frac{perpendicular side }{Base}$

$tan35.5^{\circ}=\frac{AB}{BC}$

$0.713=\frac{10}{BC}$

$BC=\frac{10}{0.713}$

BC=14.02m

In triangle EBD

EB=14 m

$\theta=54.5^{\circ}$

$tan54.5=\frac{EB}{BD}$

$1.4019=\frac{14}{BD}$

$BD=\frac{14}{1.4019}$

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.

Answer 2

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.