Two walkers set off at the same time from a cross road and walk along flat straight roads inclined to each other at 70 degree. If they both walk at a speed of 8km/h , find their distance apart 10 minutes later.

Answer 1

To find the distance apart of the two walkers, we need to first find the distance each walker has traveled in 10 minutes.

Since both walkers are walking at a speed of 8 km/h, in 10 minutes they would have traveled 8*(10/60) = 8/6 = 4/3 km each.

Now, we can form a triangle with the distance each walker has traveled as two sides of the triangle and the angle between the roads as 70 degrees. The distance apart of the two walkers can be found using the law of cosines:

d^2 = (4/3)^2 + (4/3)^2 - 2 * (4/3) * (4/3) * cos(70 degrees)
d^2 = (16/9) + (16/9) - 2 * (16/9) * (16/9) * cos(70 degrees)
d^2 = 32/9 - (512/81) * cos(70 degrees)

Now, we can calculate the distance apart by substituting the value of cos(70 degrees) ≈ 0.3420:

d^2 = 32/9 - (512/81) * 0.3420
d^2 = 32/9 - 0.1170
d^2 = 32/9 - 0.1170
d^2 ≈ 3.5756
d ≈ 1.8905 km

So, the walkers are approximately 1.8905 km apart after 10 minutes.