A plane flies in a direction of 85° from Chicago. It then turns and flies in the direction of 200° for 150 miles. It is then 195 miles from its starting point. How far did the plane fly in the direction of 85°?
I am confused about aereal navigation. Can someone help me?
Thank you a lot you saved my life.
I don't understand where do you get the 65 from?
Sure, I can help you with that. To find the distance the plane flew in the direction of 85°, we can use trigonometry. Let's break down the problem step by step:
1. Start by drawing a diagram to visualize the situation. Label Chicago as the starting point (let's call it point A), and mark a line in the direction of 85°. This represents the initial path of the plane.
2. Now, imagine the plane turning and flying in the direction of 200° for 150 miles. Mark this as a line segment on your diagram, starting from the end point of the previous line (let's call this point B).
3. Given that the plane is then 195 miles from its starting point, draw a straight line connecting point A and point B. This forms a right-angled triangle.
4. Let's call the distance the plane flew in the direction of 85° as 'x'. This will be the length of the side adjacent to the angle of 85° in the right-angled triangle.
5. Now, we can use trigonometry to find 'x'. Specifically, we will use the cosine function. The cosine of an angle in a right-angled triangle is equal to the adjacent side divided by the hypotenuse.
So, cos(85°) = x / 195
6. Rearrange the equation to solve for 'x':
x = cos(85°) * 195
Use a calculator to find the value of cos(85°) and multiply it by 195 to get the distance the plane flew in the direction of 85°.
Following this process, the plane flew approximately 35.6 miles in the direction of 85°.
I made a sketch with Chicago as C, A as the end of the first flight, and B as the end of the 2nd flight.
In triangle ABC
AC = x, AB = 150, BC = 195, angle A = 65°
by the sine law:
sinC/150 = sin 65/195
sinC = .69715...
C = 44.199... (I stored that in calculator's memory)
then angle B = 180 - 65 - 11.199.. = 70.8004...
again, by the sine law,
x/sin70.8004.. = 195/sin65
x = 203.19 miles