An aeroplane flies 125 km in the direction 110°.It then changes course a and flies for 170km in the direction of 160°.Find by calculation it's distance from the starting point.

Answer 1

To find the distance from the starting point, we can use the cosine rule.

Let's call the starting point O, the point after the first leg A, and the final point after the second leg B.

First, let's find the coordinates of points A and B using trigonometry:

For point A:
x = 125*cos(110°)
y = 125*sin(110°)

For point B:
x = 125*cos(110°) + 170*cos(160°)
y = 125*sin(110°) + 170*sin(160°)

Now, we can find the distance from the starting point O to the final point B using the distance formula:

distance = sqrt[(x^2) + (y^2)]

Substitute the values of x and y for point B into the formula and calculate the distance.

distance = sqrt[(125*cos(110°) + 170*cos(160°))^2 + (125*sin(110°) + 170*sin(160°))^2]

distance ≈ 310.21 km

Therefore, the distance from the starting point to the final point is approximately 310.21 km.