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

The value of x=4 meters.

Explanation:

Let DC=x m

In triangle ABC

`\theta=35.5{\circ}`

AB=10 m

We know that

`tan\theta=(perpendicular side )/(Base)`

`tan35.5^(\circ)=(AB)/(BC)`

`0.713=(10)/(BC)`

`BC=(10)/(0.713)`

BC=14.02m

In triangle EBD

EB=14 m

`\theta=54.5^(\circ)`

`tan54.5=(EB)/(BD)`

`1.4019=(14)/(BD)`

`BD=(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.