# Pls helpit? Two ships are sailing from the pier. X ship is sailing due east and the O ship is sailing 43 degrees South of East. After an hour, X ship had traveled 115kms and O ship has traveled 98kms. How far apart are they? thanks. Could u pls provide a solution on how u solved Thank u very much..

2
by gypsy0509

• Brainly User
2015-09-04T09:58:18+08:00

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Distance between the location after one hour of Ship X and O that traveled to different direction 43 degrees from the pier (origin).

The sketch is a triangle, where the angle 43 degrees is between two sides (distances) 115 km and 98 km.

Notice that the angle is between two sides (if you sketch it, it's an angle depression)

Use Law of Cosines to find the third side (distance)

Let a and b are the sides, and cosine theta = 43 degrees.

a = 115      b = 98                   theta = 43 degrees

c² = a² + b² - 2(a)(b)(cosC)

c² = (115)²  + (98)² - 2 (115)(98)(cos 43degrees)
c² = 13 225 + 9 604 - 22 540 (0.707)
c² =  22 829 - 15 935.78
c² =  6 893.22

c = 83.025
c = 83 kms.

The distance between the two ships at 45 degrees after one hour is 83 km.

(I hope this helps)
2015-09-04T16:04:01+08:00
A²=b²+c²-2(b)(c) Cos A
a²=98²+115²-2(98)(115) Cos 47°
a=√7456.76
a=86.35 miles

115/sinC = 86.35/Sin47°
Sin C = Sin47°(115)/86.35              C= 76°.91

∠B= 180°-∠A+∠C
= 180°-47°+76°.91
= 56°.09