please help on math?

The crows nest of a pirate ship is 22m above the water level. A pirate sitting at the crows nest spots a dolphin at an angle of depression of 15 degrees, in the direction of South 20 degrees East. He also spots a shark at an angle of depression of 23 degrees in the direction of South 45 degrees east. How many meters is the dolphin from the shark?

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  • sepia
    Lv 7
    5 months ago

    The crow's nest of a pirate ship is 22 m above the water level.

    A pirate sitting at the crow's nest spots a dolphin at an angle of depression of 15°,

    in the direction of South 20° East.

    He also spots a shark at an angle of depression of 23° in the direction of South 45° East.

    How many meters is the dolphin from the shark?

    Let d be the distance of the dolphin from the shark.

    The dolphin is at a distance of 22 / tan 15° or 82.1051 m

    The shark is at a distance of 22 / tan 23° or 51.8288 m

    The angle between the dolphin and the shark = 45° - 20° = 25°

    d^2 = 82.1051^2 + 51.8288^2 - 2*82.1051*51.8288 cos 25°

    d^2 = 1714 m, d = 41.40048... m

    The dolphin is at a distance of 41.4 meters from the shark.

  • Mike G
    Lv 7
    5 months ago

    d = distance to dolphin = 22/tan15 = 82.1051 m

    s = distance to shark = 22/tan23 = 51.8288 m

    Angle between them = 45-20 = 25°

    Cosine Rule

    x = distance required

    x^2 = 82.1051^2 + 51.8288^2 - 2*82.1051*51.8288cos25

    x = 41.4 m

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