A ship's sonar locates a treasure chest at a 12° angle of depression. A diver is lowered 40 meters to the ocean floor. How far (to the nearest meters) does the diver need to swim along the ocean floor to get the treasure chest?

Question

Mathematics

Renee Chambers

25 January, 12:16

A ship's sonar locates a treasure chest at a 12° angle of depression. A diver is lowered 40 meters to the ocean floor. How far (to the nearest meters) does the diver need to swim along the ocean floor to get the treasure chest?

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Answers (1)

Know the Answer?

Janessa Bradshaw · Answer 1

The answer to your question is 8.5 m

Step-by-step explanation:

Data

angle = Ф = 12°

dept = 40 m

distance from the ship to the treasure = ?

Process

To solve this problem use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is tangent.

tan Ф = Opposite side / Adjacent side

-Solve for Opposite side

Opposite side = Adjacent side x tanФ

-Substitution

Opposite side = 40 x tan 12

-Simplification

Opposite side = 8.5 m