Helicopter A is flying due north toward a landing point 10 miles away. Helicopter B is 11 miles due east of helicopter A. About how far is helicopter B from the landing point?
A (instantaneously), B and the landing point (of A) are the vertices of a right triangle.
The distance between B and the landing point is:
sqrt[(10)^2 + (11)^2] = 14.87 miles
To find the distance between helicopter B and the landing point, we can use the Pythagorean theorem, which 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 distance between helicopter B and the landing point is the hypotenuse, and the distances between helicopter B and helicopter A, as well as between helicopter A and the landing point, are the other two sides.
Let's consider helicopter B as point B, helicopter A as point A, and the landing point as point L.
The distance between helicopter B and helicopter A (AB) is 11 miles (the given distance).
The distance between helicopter A and the landing point (AL) is 10 miles (the given distance).
To find the distance between helicopter B and the landing point (BL), we can use the Pythagorean theorem:
BL^2 = AB^2 + AL^2
BL^2 = 11^2 + 10^2
BL^2 = 121 + 100
BL^2 = 221
Taking the square root of both sides to solve for BL:
BL = √221 ≈ 14.87 miles
Therefore, helicopter B is approximately 14.87 miles away from the landing point.
To determine how far helicopter B is from the landing point, we need to use the Pythagorean theorem, which 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 lengths of the other two sides.
In this case, helicopter A is flying due north, so we have a right triangle with helicopter A at the vertex of the right angle, the landing point as one of the sides, and helicopter B as the hypotenuse of the triangle.
Given that helicopter A is flying due north toward the landing point 10 miles away and helicopter B is 11 miles due east of helicopter A, we can create a right-angled triangle.
To find the distance between helicopter B and the landing point, we can consider the horizontal distance (11 miles due east) and the vertical distance (10 miles due north) as the two sides of the right triangle. Let's call the horizontal distance (11 miles) side "a" and the vertical distance (10 miles) side "b".
Using the Pythagorean theorem, we can calculate the length of the hypotenuse (c), which represents the distance between helicopter B and the landing point:
c^2 = a^2 + b^2
c^2 = 11^2 + 10^2
c^2 = 121 + 100
c^2 = 221
To find the value of c (the distance between helicopter B and the landing point), we take the square root of both sides:
c = √221
c ≈ 14.87
Therefore, helicopter B is approximately 14.87 miles away from the landing point.