A man travels 24km due north and then 7km due west.what is his bearing from the starting point correct to the nearest degree
Well, let's see. If a man travels 24km due north and then 7km due west, his journey forms a right-angled triangle. To find his bearing, we need to determine the angle between his original direction (north) and the line connecting his final position to the starting point (west).
Now, the tangent of an angle in a right-angled triangle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, the opposite side is 7km (west) and the adjacent side is 24km (north).
So, let's use our math skills and find the tangent of the angle:
tan θ = opposite/adjacent = 7/24
Now, if we take the inverse tangent (arctan) of this ratio, we can find the angle:
θ = arctan (7/24) ≈ 16.26 degrees
Therefore, the man's bearing from the starting point is approximately 16 degrees. However, as a Clown Bot, I have to ask, is he also carrying a compass or just a really good sense of humor?
To find the bearing from the starting point, we can use basic trigonometry.
Step 1: Draw a diagram of the journey.
Considering the man starts at point A, travels 24km due north, then 7km due west, we can label the final position as point B.
24km
A -------------- B
7km
Step 2: Find the distance between the starting and ending points.
Using the Pythagorean theorem, we can find the distance between A and B.
Distance = square root of (24² + 7²) = square root of (576 + 49) = square root of 625 = 25 kilometers
Step 3: Calculate the angles using trigonometry.
To find the bearing, we need to find the angle that the line AB makes with the north direction.
First, we find the angle that the line AB makes with the east direction (the horizontal line).
Using tangent: tangent of angle A = opposite/adjacent = 7/24
Angle A = tan^-1(7/24) = 16.66 (rounded to the nearest degree)
Next, we find the angle that the line AB makes with the north direction.
Since the line AB makes an angle of 90 degrees with the east direction, we subtract this angle from 90 degrees.
Angle = 90 - 16.66 = 73.34 degrees (rounded to the nearest degree)
Therefore, the man's bearing from the starting point is 73 degrees (to the nearest degree).
To determine the man's bearing from the starting point, we can use trigonometry and the concept of right triangles.
First, let's visualize the situation. We have a right triangle, where the man traveled 24 km north (the vertical side) and 7 km west (the horizontal side). The hypotenuse of this triangle represents the straight-line distance between the man's current position and the starting point.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
h² = 24² + 7²
h² = 576 + 49
h² = 625
h = √625
h = 25
So, the length of the hypotenuse is 25 km.
Now, let's find the angle that the hypotenuse makes with the north direction. We can use the inverse tangent function (arctan) to get the angle:
tan(θ) = opposite/adjacent
tan(θ) = 7/24
θ = arctan(7/24)
Using a calculator, we find that θ ≈ 16.3 degrees.
However, this angle is measured with respect to the north direction. To find the bearing, we need to consider the angle clockwise from the north direction to the hypotenuse.
Since the man traveled due north, the bearing with respect to the starting point is the complement of the angle we found. Subtracting the angle from 90 degrees, we get:
Bearing = 90 degrees - θ
Bearing = 90 - 16.3
Bearing ≈ 73.7 degrees
So, the man's bearing from the starting point is approximately 73.7 degrees, correct to the nearest degree.