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?
answer:
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?
c^2 = 900^2+1260^2-2(900)(1260)(cos75) correct
= 810,000 + 1,587,600 - 587,001.59
= 1,810,598.4 (you had 33542.9)
c = √1,810,598.4
c = 1345.58
Yes, your calculation is correct. You used the formula c^2=a^2+b^2-2ab cos C to find the distance c between the two planes. Here's a step-by-step explanation of how you arrived at the answer:
1. First, let's assign labels to the variables:
- The speed of the first plane is 300 km/h. Let's call the distance it travels in 3 hours as a.
- The speed of the second plane is 420 km/h. Let's call the distance it travels in 3 hours as b.
- The angle between their flight paths is 75 degrees. Let's call this angle C.
2. Using the given information, we can calculate the distances traveled by each plane in 3 hours:
- The distance traveled by the first plane: a = 300 km/h * 3 h = 900 km.
- The distance traveled by the second plane: b = 420 km/h * 3 h = 1260 km.
3. Now, let's substitute the values into the formula c^2 = a^2 + b^2 - 2ab cos C:
- c^2 = 900^2 + 1260^2 - 2(900)(1260)(cos 75°).
4. Calculate the expression inside the parentheses:
- 2(900)(1260)(cos 75°) ≈ 2(900)(1260)(0.258819) ≈ 589,590.
5. Substitute the value of the expression back into the formula:
- c^2 = 900^2 + 1260^2 - 589,590.
6. Calculate the right side of the equation:
- c^2 ≈ 810,000 + 1,588,400 - 589,590.
- c^2 ≈ 1,808,810.
7. Finally, take the square root of both sides to find the distance c:
- c ≈ √(1,808,810).
- c ≈ 1346.47 km.
Therefore, the planes are approximately 1346.47 km apart after three hours. Your answer of c = 183.14 km seems to be incorrect, as it is significantly smaller than the expected result.