Two airplanes leave an airport at the same time. One travels at 355km/h and the other at 450km/h. Two hrs later they are 800km apart. Find the angle between their courses.
a^2 = b^2 + c^2 - 2bc Cos A
800^2= 450^2 + 355^2 - 2(450)(355) Cos A
640000= 202 500 + 126 025 - 319 500 Cos A
640 000-328 525 = -319 500 Cos A
311 475= -319 500 Cos A
311 475/ -319 500= Cos A
-0.9749= Cos A
167.13 = A
Can you please explain to me what is wrong with this? I checked the back of the book and the answer is suppose to be 58.17
thanks~!
A quick look finds that you missed the fact that the time the airplanes are 800km apart is 2 hours not 1 hour. The legs should be 2*355km and 2*450km.
hi, so should I multiply 202 500 and 126 025 by 2?
Actually, you would have to multiply them by 4 because they are squared. You have the right idea.
For the legs use:
b=2*450km=900km
c=2*355km=710km
This would then give you
800^2=900^2 + 710^2 - 2(900)(710)cos(A)
Solve for A using the same method you did before.
ohh, okay. thank you!
Glad to help!
In order to find the angle between the courses of the two airplanes, you need to use the Law of Cosines. However, there seems to be a mistake in your calculations. Let's go through the steps again:
Given information:
Speed of the first airplane (a) = 355 km/h
Speed of the second airplane (b) = 450 km/h
Time elapsed = 2 hours
Distance covered by the airplanes (c) = 800 km
Angle between their courses = A (what we're trying to find)
To start, we can calculate the distance covered by each airplane using the formula Distance = Speed × Time:
Distance covered by the first airplane = 355 km/h × 2 hr = 710 km
Distance covered by the second airplane = 450 km/h × 2 hr = 900 km
Now, let's draw a triangle to represent the situation, where the sides of the triangle represent the distances traveled by each airplane and the angle between their courses is A.
We know the following sides:
Side a = 710 km
Side b = 900 km
Side c = 800 km (the distance between the two airplanes)
To find the angle A, we can use the Law of Cosines, which states that:
c² = a² + b² - 2ab cos(A)
Let's substitute the given values:
800² = 710² + 900² - 2(710)(900) cos(A)
640,000 = 504,100 + 810,000 - 1,278,000 cos(A)
640,000 = 1,314,100 - 1,278,000 cos(A)
1,278,000 cos(A) = 1,314,100 - 640,000
1,278,000 cos(A) = 674,100
cos(A) = 674,100 / 1,278,000
cos(A) = 0.5270
To find the angle A, use the inverse cosine function (cos^(-1)) on both sides of the equation:
A = cos^(-1)(0.5270)
Using a calculator, you will get:
A ≈ 58.17 degrees
So the correct answer is approximately 58.17 degrees, which matches the answer mentioned in the book.