Two Planes leave an airport at the same time, one flying 300km/h and the other at 420km/h
The angle between their flight paths is 75 degrees after three hours, how fart apart are they?
so it would be c^2=a^2+b^2-2ab cos C
900^2+1260^2-2(900)(1260)(cos75)
c^2=33542.9
c=183.14km
is it right?
I don't see your answer to check.
The law of cosines would work well on this problem. You know two sides (900 and 1260 km) and the included angle (75 deg) of a triangle.
thanks
No. It isn't right. See my answer to your later post.
To calculate the distance between the two planes after three hours, we can use the concept of relative velocity and some basic trigonometry.
Step 1: Find the distance traveled by each plane after three hours.
The distance traveled by the first plane is calculated by multiplying its speed (300 km/h) by the time (3 hours):
Distance1 = Speed1 * Time = 300 km/h * 3 hours = 900 km
Similarly, the distance traveled by the second plane is:
Distance2 = Speed2 * Time = 420 km/h * 3 hours = 1260 km
Step 2: Find the horizontal and vertical components of the distances traveled by each plane.
Since we are dealing with a triangle, we need to split the distances into their horizontal and vertical components.
For the first plane:
Horizontal distance1 = Distance1 * cos(angle)
Vertical distance1 = Distance1 * sin(angle)
For the second plane:
Horizontal distance2 = Distance2 * cos(180 - angle)
Vertical distance2 = Distance2 * sin(180 - angle)
Step 3: Calculate the horizontal and vertical distances between the two planes.
To find the actual horizontal and vertical distances between the two planes, we subtract the corresponding components:
Horizontal distance = Horizontal distance2 - Horizontal distance1
Vertical distance = Vertical distance2 - Vertical distance1
Step 4: Use the Pythagorean theorem to calculate the distance between the planes.
The distance between the two planes is given by the hypotenuse of the triangle formed by the horizontal and vertical distances. We can use the Pythagorean theorem to find this distance:
Distance between planes = sqrt((Horizontal distance)^2 + (Vertical distance)^2)
By substituting the horizontal and vertical distances from Step 3 into the above formula, you can calculate the distance between the two planes.
Please note that for precise calculations, it is important to use radians instead of degrees in trigonometric functions. However, for simplicity, I have assumed degrees in the explanation.