A helicopter flies in a straight line until it reaches a point 20 km east and 15 km north of its starting point. It then turns through 90° and travels a further 10 km.
(a)
How far is the helicopter from its starting point?
plot the points and then use the usual distance formula.
33.54km
To find the distance of the helicopter from its starting point, we can use the Pythagorean Theorem.
The helicopter flies 20 km east and 15 km north, forming a right-angled triangle. The distance from the starting point to the final point is the hypotenuse of this triangle.
Using the Pythagorean theorem:
hypotenuse^2 = (base)^2 + (height)^2
So, hypotenuse^2 = 20^2 + 15^2
hypotenuse^2 = 400 + 225
hypotenuse^2 = 625
Taking the square root of both sides, we get:
hypotenuse = √625
hypotenuse = 25
Therefore, the helicopter is 25 km away from its starting point.
To find out how far the helicopter is from its starting point, we can use the Pythagorean theorem.
The Pythagorean theorem 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, the helicopter has traveled 20 km east and 15 km north, forming a right triangle with these distances as two sides. We can label the distance from its starting point to the point 20 km east as side A and the distance from its starting point to the point 15 km north as side B. The distance we are trying to find is the hypotenuse, which we'll label as C.
Using the Pythagorean theorem, we can write the equation:
A^2 + B^2 = C^2
Substituting the given values:
(20 km)^2 + (15 km)^2 = C^2
400 km^2 + 225 km^2 = C^2
625 km^2 = C^2
We can now take the square root of both sides to find C:
C = sqrt(625 km^2)
C = 25 km
Therefore, the helicopter is 25 km away from its starting point.