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

Answer 1

To solve this problem, we can use trigonometry to find the distance between the two walkers after 10 minutes.

First, we need to find the distance each walker has traveled in 10 minutes:

Distance = Speed x Time
Distance = 8 km/hr x (10/60) hr
Distance = 8/6 km
Distance = 4/3 km

Since the two walkers are walking at an angle of 70 degrees to each other, we can consider the distance between them as the hypotenuse of a right triangle with legs of 4/3 km each.

Using trigonometry, we can calculate the distance between them:
Distance apart = sqrt((4/3)^2 + (4/3)^2 - 2(4/3)(4/3)cos(70))
Distance apart = sqrt((16/9) + (16/9) - 2(16/9)(16/9)cos(70))
Distance apart = sqrt(32/9 - 64/81(cos70))
Distance apart = sqrt(32/9 - 64/81(0.342))
Distance apart = sqrt(32/9 - 0.073)
Distance apart = sqrt(3.56)
Distance apart ≈ 1.888 km

Therefore, after 10 minutes, the two walkers will be approximately 1.888 km apart.