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juin [17]
3 years ago
5

Every day going to school, June has to go by boat (point A) over a 217m-wide river to point B (the other bank), and then from B

walk to school at point D with distance AD ​​= 170m. In fact, due to the flowing water, the boat was pushed by the water at an angle of 50 degrees and brought her to point C (the other shore). From C, June walk to school. Calculate the distance June traveled from A to D. (result rounded to the third decimal place)​

Mathematics
1 answer:
Anit [1.1K]3 years ago
4 0

Answer:

  • 647m

Explanation:

The distance traveled by June, from A to D, is the sum of the distance from A to C plus the distance from C to D:

  • Travel from A to D = Distance AC + Distance DC.

<u>1) Find the distance AC</u>

  • Triangle ABC is a right triangle, from which you have to calculate the hypotenuse (AC), knowing angle A (50º), and its adjacent leg (217 m).
  • cos (50º) = 217m / AC
  • AC = 217m / cos (50º) = 337.59m

<u>2) Find the distance DC</u>

First, you need to calculate the side BC which is a common side of both triangles ABC and DBC.

You can use Pythagora's or a trigonometric function (tangent or sine).

  • tan (50º) = BC / 217 m ⇒ BC = 217 m × tan (50º) = 258.61 m

Now you can use Pythagora's theorem to find the distance DC, which is the hypotenuse of the triangle DBC:

  • DC² = (170m)² + (258.62)² = 95,779.41m²
  • DC = 309.48m

<u>3) Find the total distance traveled from A to D</u>

  • Travel from A to D = Distance AC + Distance DC = 337.59m + 309.48m = 647.07 m ≈ 647m.
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