# After travelling south for 7 1/2 h, how far is the ship from the port in terms of the Pythagorean Relationship?a ship leaves port heading due west. After traveling at a speed of 20km/h for 10 h,...

After travelling south for 7 1/2 h, how far is the ship from the port in terms of the Pythagorean Relationship?

a ship leaves port heading due west. After traveling at a speed of 20km/h for 10 h, the ship makes a 90 degree turn and heads south, travelling at the same speed. After travelling south for 7 1/2 h, how far is the ship from the port?

Can someone please explain the question to me?

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### 1 Answer

Step 1: Find the distance covered heading due west.

d = rt

d = 20 (10 )

d = 200 km

Step 2: Find the distance traveling south after making a 90 degree turn. Note that the 90 degree turn has "set up" a right triangle.

d = rt

d = (20)(7.5)

d = 150 km

Step 3: THINK! The legs of the right triangle formed by traveling due west and then south are 200 km. and 150 km. Use the Pythagorean Theorem to find the hypotenuse of the right triangle which will be the distance between the ship and the port.

Step 4: c ^2 = a^2 + b^2

c ^2 = {(200) ^ 2} + {(150) ^2}

c ^2 = 40000 + 22500

c ^2 = 62500

c = sqrt 62500

c = 250 km

**The answer is 250 km.**