Two walkers set off at the same time from a crossroad and walk along flat straight roads inclined to each other at 68 degrees.If they both walk at a speed of 6km/h,find their distance apart 10 minutes later.
In 10 minutes they each walk 6/6 = 1km
d^2 = 1^2 + 1^2 - 2(1)(1)cos68°
Find their distance apart in 10 minutes later using the trigonometry ratio
1 kilometer
Correct! The distance between them after 10 minutes is approximately 1 kilometer.
Well, if there's anything I know about walkers, it's that they tend to chat and take their time. So, let's assume these walkers decide to take a nice, leisurely stroll and have a silly conversation while walking.
Now, if the walkers are inclined to each other at 68 degrees, it means they are forming an isosceles triangle. The angle between them is 180 - 68 - 68 = 44 degrees.
Since both walkers are going at the same speed of 6 km/h, we can calculate their distance covered in 10 minutes.
10 minutes is equal to 10/60 = 1/6 hours.
The distance covered by each walker in 1/6 hour is 6/6 = 1 km.
Now, let's imagine this conversation between the walkers:
Walker 1: "Hey, Walker 2, how far apart do you think we are?"
Walker 2: "Oh, I don't know, but I guess we could use some basic trigonometry to find out!"
Walker 1: "Brilliant suggestion! Let's do it!"
Since the angle between them is 44 degrees and they covered a distance of 1 km, we can use the sine function to find the distance between them.
sin(44) = distance between them / 1 km
Solving for the distance between them, we get:
distance between them = 1 km * sin(44)
Plugging this into a calculator, we find that the distance between them is approximately 0.709 km.
So, after 10 minutes of walking at 6 km/h, these two silly walkers are approximately 0.709 km apart.
To find the distance apart between the two walkers, we need to calculate the distance each walker travels in 10 minutes and then find the distance between them using trigonometry.
First, let's calculate the distance each walker travels in 10 minutes. The speed is given as 6 km/h, which means they travel 6 kilometers in one hour. To find the distance traveled in 10 minutes, we can use the formula:
Distance = Speed × Time
Therefore, the distance each walker travels in 10 minutes is:
Distance = (6 km/h) × (10 minutes / 60 minutes)
Simplifying and converting units:
Distance = (6 km/h) × (1/6 hours)
Distance = 1 km
Now that we know each walker has traveled 1 kilometer, we can use trigonometry to find their distance apart.
Since the roads the walkers are on are inclined to each other at an angle of 68 degrees, we can consider this as a triangle where the distance between the walkers is the side opposite the 68-degree angle.
Let's call this side 'd' (distance apart). We can use trigonometry's sine function to find 'd':
sin(θ) = opposite/hypotenuse
sin(68 degrees) = d/1
To find 'd', we rearrange the equation:
d = 1 × sin(68 degrees)
Using a calculator, we find:
d ≈ 0.927 km
Therefore, the distance between the two walkers 10 minutes later is approximately 0.927 kilometers.