Question

Two trains leave a station on different tracks. The tracks make an angle of 130°, with the station as a vertex. The first train travels 100 km and makes its first stop at point A, while the second train travels 200 km and makes it first stop at point B. How far apart are the trains when both are at their first stop? Round the answer to the nearest integer.

Answer 1

d=275

Explanation:

d^2=a^2+b^2-2(a)(c)cos(130)

d^2=100^2+200^2-2(100)(200)cos(130)

d^2= 50,000-(-25711.5)

d^2=75711.5

d=approximately 257

Answer 2

The first train, let’s call this train A, covers a distance of 100 km. dA = 100 km

The second train, train B, covers a distance of 200 km. dB = 200 km

The Law of Cosine states that:

c^2 = a^2 + b^2 – 2abcos ø

Where a = dA , b = dB, and ø = 130° angle between them

c^2 = 100^2 + 200^2 – 2(100)(200)cos130

Using the calculator:

c^2 = 64691.65

c = 254. 35 km rounding off:

c = 254 km

Therefore the 2 trains are 254 km apart after their 1st stop.