A navigator plots the course a plane is currently traveling. The plane is 300 miles from its destination. If it continues on its
current course it will travel 325 miles and end up 125 miles due south of its destination. To the nearest degree, how many degrees is the plane off course?
1 answer:
We have to use the rule of cosx° to solve this problem. Attached is a diagram of the navigator's course for the plane. It is similar to the shape of a triangle. We know the plane is 300 miles from its destination, so that will be one of the sides. On the current course, it is 325 miles from its destination, so that will be another one of the sides. The last side is 125 because that is the distance between the destination and the anticipated arrival. Cosx° is what we are looking for.
To find how many degrees off course the plane is, we must use the rules of Cosx°, which is shown in the attached image.
The plane is approximately 23° off course.
To find how many degrees off course the plane is, we must use the rules of Cosx°, which is shown in the attached image.
The plane is approximately 23° off course.
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Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.
What is Pythagoras Theorem?
The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.
The formula for Pythagoras Theorem is given by,
Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.
Each Subtraction in view of Pythagoras Theorem
It is is given that,
or
Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.
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