Question

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 ? ?

Answer 1

KL = 12km s° = 59°

SL = 9.72km l° = 77°

SK = 13.6km k° = 44°

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