Observers in two lighthouses K and L spot a ship S.

Mathematics

1 answer:

BaLLatris [955]2 years ago

4 0

Answer:

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.

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°

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

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