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a plane flies 1.7 hours at 130 mph on a bearing of 20°. it then turns and flies 4.7 hours at the same speed on a bearing of 110°. How far is the plane from its starting point. (round to the nearest mile)

User KingArasan
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1 Answer

14 votes
14 votes

Answer

The distance of the plane from its starting point = 650 miles

Step-by-step explanation

We will call the position the plane started from the starting point.

The next place the plane flew to is then the intermediate point.

And the final position of the plane is the final point.

To draw the image of this, we need to then calculate the length of each of the plane's travels.

Speed = (Distance)/(Time)

Cross multiply and we have

Distance = (Speed) (Time)

From the starting point to the intermediate point, the plane flies 1.7 hours at 130 mph

Distance = (Speed) (Time)

Speed = 130 mph

Time = 1.7 hours

Distance = (Speed) (Time)

Distance = (130) (1.7) = 221 miles

Then the plane flies for 4.7 hours at the same speed (130 mph) from the intermediate point to the final point.

Distance = (Speed) (Time)

Speed = 130 mph

Time = 4.7 hours

Distance = (Speed) (Time)

Distance = (130) (4.7) = 611 miles

So, the image representing the total motion of the plane is presented below.

Let the distance of the plane from its starting point (distance between final point and starting point) be x.

We can see that the motion forms a triangle with one of the angles equal to 90 degrees, meaning that this triangle is a right angle triangle. Hence, we can solve for x, by applying Pythagoras theorem.

The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

a = 221 miles

b = 611 miles

hyp = x = ?

a² + b² = (hyp)²

221² + 611² = x²

48,841 + 373,321 = x²

422,162 = x²

x² = 422,162

Take the square root of both sides

√(x²) = √(422,162)

x = 649.74 = 650 miles to the nearest mile.

Hope this Helps!!!

a plane flies 1.7 hours at 130 mph on a bearing of 20°. it then turns and flies 4.7 hours-example-1
User AshleyS
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