Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Two points A and C are on the same level ground as the foot of pole B . The distance between A and C is 40m and A and C are on the same sides of the vertical pole . The distances from the top of the pole D to A and C are 53 and 85 respectively. Find correct to 1 do the distance between the foot of the pole B and the point A.

Sagot :

atashinchiii

Answer:

The distance between the pole and point A is 35.2m

Step-by-step explanation:

First, we have to illustrate the problem. I can't draw as of the moment but I'll try my best to describe the drawing as best as I can. You can draw this in a scratch paper to have a better understanding.

  • In a horizontal line, there is a point A, B, and C.
  • From left going to right, the arrangement of points will be C-A-B.
  • The distance between A and C is 40m.
  • The pole is standing at point B with height h.
  • The tip of the pole or the top most part of the pole is point D.
  • From point D to A, the measurement is 53m.
  • From point D to C, the measurement is 85m.
  • Let's name the distance between A and B as x.

Now that you have drawn this. There should be two triangles formed now namely triangle DCB and DAB.

TRIANGLE DCB

By Pythagorean Theorem, we can write an equation for the height of the pole.

[tex]h^{2} = {53}^{2} - {x}^{2} [/tex]

TRIANGLE DAB

By Pythagorean Theorem, we can write an equation for the height of the pole.

[tex] {h}^{2} = {85}^{2} - {(40 + x)}^{2} [/tex]

Since we only have one pole, this means that we can equate the two equations.

[tex] {53}^{2} - {x}^{2} = {85}^{2} - {(40 + x)}^{2} \\ {53}^{2} - {85}^{2} = {x}^{2} - ( {x}^{2} + 80x + 1600) \\ - 4416 = - 80x - 1600 \\ 80x = 4416 - 1600 \\ 80x = 2816 \\ x = \frac{2816}{80} \\ x = 35.2[/tex]

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.