A man travels 7 km due north and then 9 km due east. At end of his journey find his bearing from starting point.
Is it adding? Or pythagorean theorem?
is it correct AR= 9-7=2 km
whereby final answer 9.21 km
its not pythagorean i already tried to do it dosnt work
You want the angle... not the side length.
Ah, now I understand- the angle.
Now a question for you, do you remember which trig function to use??
You have a right-angled triangle,
distance travelled = √(81 + 49) = appr 11.4 km
tanØ = 9/7
Ø = appr 52.1°
To find the bearing of the man from the starting point, we can use trigonometry and the concept of right triangles.
First, let's draw a diagram to visualize the situation. We have a right-angled triangle where the northern leg is 7 km long and the eastern leg is 9 km long. The hypotenuse of this triangle represents the straight-line distance between the starting point and the end point, which will help us find the bearing.
Using the Pythagorean theorem, we can find the length of the hypotenuse (H):
H² = (Northern leg)² + (Eastern leg)²
H² = 7² + 9²
H² = 49 + 81
H² = 130
H ≈ √130
H ≈ 11.4 km (approx.)
Now, let's find the angle that the line connecting the starting point and the end point makes with the northern direction. We can use trigonometry to find this angle.
Tangent of the angle = (Eastern leg) / (Northern leg)
Tangent of the angle = 9 / 7
Angle = arctan(9 / 7)
Angle ≈ 52.9° (approx.)
To get the bearing, we need to express the angle in terms of compass directions. The bearing is measured clockwise from the north direction.
Since the line is 52.9° clockwise from the north direction, we subtract this angle from 90° to get the bearing:
Bearing = 90° - 52.9°
Bearing ≈ 37.1° (approx.)
So, the man's bearing from the starting point is approximately 37.1°.