An airplane is flying at an altitude of 10,000m. The pilot sees two ships A and B. Ship A is due south of P and 22.5km away (in a direct line).Likewise ship B is due East and 40.8km from P. Find the distance between the two ships.
To find the distance between the two ships, we can use the Pythagorean theorem. We have a right-angled triangle formed by the airplane, ship A, and ship B.
Let's denote the distance between the airplane and ship A as "x", and the distance between the airplane and ship B as "y".
We know that x = 22.5 km and y = 40.8 km.
Using the Pythagorean theorem, we have:
hypotenuse^2 = x^2 + y^2
Since the hypotenuse is the distance between ship A and ship B, we'll denote it as "d".
Therefore, d^2 = (22.5 km)^2 + (40.8 km)^2
d^2 = 506.25 km^2 + 1664.64 km^2
d^2 = 2170.89 km^2
Now, we'll take the square root on both sides to find the distance "d":
d = √(2170.89 km^2)
d ≈ 46.62 km
So, the distance between ship A and ship B is approximately 46.62 km.
To find the distance between the two ships, we can use the Pythagorean theorem.
First, let's create a diagram to visualize the given information:
A
|
P----|----
|
B
We have a right triangle formed by the airplane (P), Ship A, and Ship B. The distance between Ship A and Ship B is the hypotenuse of this triangle.
Using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the lengths of the two legs, and c is the length of the hypotenuse, we can find the distance between the two ships.
In this case, the length of one leg (a) is 22.5 km, and the length of the other leg (b) is 40.8 km.
Let's calculate the distance between the two ships:
a^2 + b^2 = c^2
(22.5 km)^2 + (40.8 km)^2 = c^2
506.25 km^2 + 1664.64 km^2 = c^2
2170.89 km^2 = c^2
Now, to find the distance c, we need to take the square root of both sides:
c = √2170.89 km^2
c ≈ 46.6 km
Therefore, the distance between Ship A and Ship B is approximately 46.6 km.