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Please answer this



Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown:


Two right triangles ABC and EDC have a common vertex C. Angle ABC and EDC are right angles. AB is labeled 13 feet, AC is labeled 15 feet, EC is labeled 10 feet, and ED is labeled 4 feet.


What is the approximate distance, in feet, between the two poles?


11.14 feet


16.65 feet


14.35 feet


15.59 feet

Please answer this Two poles AB and ED are fixed to the ground with the help of ropes AC and EC as shownTwo right triangles ABC and EDC have a common vertex C A class=

Respuesta :

Check the picture below.

so we can simply use the pythagorean theorem for each triangle and get "w" and "z".

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{15^2-13^2}=w\implies \sqrt{225-169}=w\implies \sqrt{56}=w\implies 7.48\approx w \\\\\\ \sqrt{10^2-4^2}=z\implies \sqrt{100-16}=z\implies \sqrt{84}=z\implies 9.17\approx z \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{w+z}{16.65}~\hfill[/tex]

Ver imagen jdoe0001
akposevictor

Applying the Pythagorean Theorem, the approximate distance in feet, between the two poles is: b. 16.65 feet

Recall:

For a right triangle where c is the hypotenuse and a and b are the other legs of the right triangle, the Pythagorean Theorem states that: c² = a² + b².

The distance between the two poles = BC + DC

Given:

  • AB = 13 feet
  • AC = 15 feet
  • EC = 10 feet
  • ED = 4 feet.

Apply the Pythagorean Theorem to find BC and DC respectively.

Length of BC:

BC = √(AC² - AB²)

  • Substitute

BC = √(15² - 13²)

BC = 7.48 feet

Length of DC:

DC = √(EC² - ED²)

  • Substitute

DC = √(10² - 4²)

DC = 9.17 feet

The distance between the two poles = 7.48 + 9.17 = 16.65 feet

Learn more about Pythagorean Theorem on:

https://brainly.com/question/18282315