Observers in two lighthouses k and l spot a ship s.

complete the diagram of the triangle formed by the lighthouses and the ship. label each measure.

k to l k to s l to s

bearing e n 44° e n 77° w

distance 12 km ? ?

KL = 12km                  s° = 59°

SL = 9.72km              l°  = 77°

SK = 13.6km               k° = 44°

Step-by-step explanation:

When you know two angles you can find the third.

1.

The angles always add to 180°:

A + B + C = 180°

so,

k ° +  s ° + l° = 180°

44 + 77 + s = 180

121 + s = 180

s = 180 - 121

s = 59°

2.

Law of Sines (the Sine Rule):

 a/sinA = b/sinB = c/sinC

KS / sin(L) = KL / sin(S)

x / sin(77) = 12 / sin(59)

x = 12 sin(77) / sin(59)

x = 13.6km

similarly,

SL / sin(k) = KL / sin(S)

y / sin(44) = 12 / sin(59)

y = 9.72km

step-by-step explanation: