a ship leaves sydney heads and travels 45 km due east. it then returns and travels 86 km due north. how far is it from its starting point?
please guys step by step.. thank you in advance.
Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2
c = sqrt ( a ^ 2 + b ^ 2 )
In this case :
a = 45
b = 86
c = sqrt ( 45 ^ 2 + 86 ^ 2 )=
sqrt ( 2025 + 7396 ) =
sqrt ( 9421 ) = 97.062 km
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To find the distance from the ship's starting point, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the ship's path to be a right triangle, with the horizontal journey of 45 km as one side and the vertical journey of 86 km as the other side.
Step 1: Draw a diagram
Draw a diagram to help visualize the problem. Label the starting point as "O" and mark the 45 km journey due east as "AB" and the 86 km journey due north as "BC." Connect points A and C to form a right triangle.
C
|\
86 km | \
| \
| \
| \
| \
| \
| \
O----A-------B
45 km
Step 2: Calculate the distances traveled
The distance traveled horizontally is 45 km (side AB), and the distance traveled vertically is 86 km (side BC).
Step 3: Apply the Pythagorean theorem
Using the Pythagorean theorem, we can calculate the distance from the ship's starting point by finding the square root of the sum of the squares of the horizontal and vertical distances.
Distance from the starting point (OC) = √(AB² + BC²)
Substituting the values, we get:
OC = √(45² + 86²)
= √(2025 + 7396)
= √9417
≈ 97.04 km
Therefore, the ship is approximately 97.04 km from its starting point.