Question

6) Two boats set off from X at the same

Answer 1

Answer:

The distance between the two boats after 2.5 hours is 57 m.

Step-by-step explanation:

The distance covered by each boat after 2.5 hours are:

speed = $\frac{distance}{time}$

distance = speed x time

For boat A, speed = 14 km/h and time = 2.5 hrs.

So that,

distance = 14 x 2.5

              = 35 km

For boat B, speed = 18 km/h and time = 2.5 hrs.

So that,

distance = 18 x 2.5

              = 45 km

The distance between the two boats after travelling 2.5 hours can be determined by applying the cosine rule. Let the distance be represented by x, so that:

$a^{2}$ = $b^{2}$ + $c^{2}$ - 2bc Cos A

$x^{2}$ = $45^{2}$ + $35^{2}$ - 2(45 x 35) Cos $90^{o}$

   = 2025 + 1225 - 3150 (0)

   = 3250

x = $\sqrt{3250}$

  = 57.0088

x = 57.0 m

The distance between the two boats after 2.5 hours is 57 m.