A student walks 50m on a bearing 025 degree and then 200m die east. How far is she from her starting point
Use the Law of Cosines:
c = sqrt[a^2 + b^2 - 2ab*cos(θ)]
c = sqrt[50^2 + 200^2 - 2(50)(200)cos(115°)]
c ≈ 225.726
Therefore, the student is 225.726 meters from her starting point
a student walks 50m on a bearing 025°and then 200m due east. how far is she from her starting point
a²=200²+50²-2*200*50*Cos 65
a=226m
Well, it seems like this student is quite adventurous! Let's see if I can calculate the distance for you.
First, let me put on my math hat. 🎩
She walked 50m on a bearing of 025 degrees, which means she moved slightly to the northeast. Then, she went 200m due east. So, we can imagine her final position as moving east from the starting point.
Now, imagine a right-angled triangle, with the distance she walked on bearing 025 degrees as one side, and the distance she walked due east (200m) as the other side.
Using some mathematical magic, we can calculate the hypotenuse, which is the straight-line distance from her starting point to her final position. And voila! The hypotenuse is the distance she is from her starting point.
So, let's do the math. 🧮
Using the Pythagorean theorem: c² = a² + b²
a = 50m (distance on bearing 025°)
b = 200m (distance due east)
c² = 50² + 200²
c² = 2500 + 40000
c² = 42500
Taking the square root of both sides gives us:
c ≈ √42500
c ≈ 206.15m
So, she's approximately 206.15 meters away from her starting point!
That's quite a trek, but hey, at least she didn't end up on the moon or something! 🌝
To find how far the student is from her starting point, we can use trigonometry.
1. Draw a diagram: Start by drawing a point to represent the student's starting point. From there, draw a line segment of 50 meters in the direction of the bearing 025 degrees. Next, draw another line segment of 200 meters to the east, starting from the endpoint of the previous line segment.
2. Find the components: The line segment of 50 meters in the bearing 025 degrees forms an angle with the x-axis (east) of 25 degrees (90 degrees - 25 degrees = 65 degrees). The line segment of 200 meters is already in the x-axis direction.
3. Calculate x and y components: For the 50-meter segment, the x-component can be found by multiplying the length (50 meters) by the cosine of the angle (25 degrees). The y-component can be found by multiplying the length (50 meters) by the sine of the angle (25 degrees). For the 200-meter segment, the x-component is 200 meters and the y-component is 0 meters (since it is in the x-axis direction).
x-component of 50-meter segment = 50 meters * cos(25 degrees)
y-component of 50-meter segment = 50 meters * sin(25 degrees)
x-component of 200-meter segment = 200 meters
y-component of 200-meter segment = 0 meters
4. Calculate the total x and y components: Add the x-components together and add the y-components together.
Total x-component = x-component of 50-meter segment + x-component of 200-meter segment
Total y-component = y-component of 50-meter segment + y-component of 200-meter segment
5. Use the Pythagorean theorem: The distance from the starting point can be found using the Pythagorean theorem with the total x and y components.
Distance = sqrt((Total x-component)^2 + (Total y-component)^2)
Plug in the values and calculate to find the distance:
Distance = sqrt((50 meters * cos(25 degrees) + 200 meters)^2 + (50 meters * sin(25 degrees) + 0 meters)^2)
After calculating, you will find the distance from the starting point.