a plane flies over a control tower at a height of 8km.an observer on the ground is 15km from the control tower.How far is the plane from the observer?
To find the distance between the plane and the observer, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length 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 height of the plane forms one side of the right triangle, the distance from the observer to the control tower forms another side, and the distance between the plane and the observer (which we want to find) forms the hypotenuse.
Let's label the distance between the plane and the observer as "d". Using the Pythagorean theorem, we have:
d^2 = (distance from observer to control tower)^2 + (height of the plane)^2
Plugging in the values:
d^2 = (15 km)^2 + (8 km)^2
d^2 = 225 km^2 + 64 km^2
d^2 = 289 km^2
To find the distance "d", we need to take the square root of both sides:
d = √(289 km^2)
d ≈ 17 km
So, the plane is approximately 17 km away from the observer.