In the same depth of the water, two scuba divers who are 20 meters apart spot a shark that is at the deeper part of the sea. The angles of depression of the shark from diver 1 and diver 2 are 47° and 40°, respectively. How far is each diver from the shark? 47⁰ 93⁰ 20 40%
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Answer:
Therefore, diver 1 is about 17.04 meters away from the shark, while diver 2 is about 22.35 meters away from the shark.
Step-by-step explanation:
To solve this problem, we can use the concept of trigonometry and set up two equations for the two scuba divers.
Let's first assume that the depth of the sea is constant and equal to "d". Then, let's denote the distance between the shark and diver 1 as "x" and the distance between the shark and diver 2 as "y". Now we can set up the following equations:
Equation 1: tan(47°) = d/x
Equation 2: tan(40°) = d/y
We can then solve these two equations simultaneously to find the values of "x" and "y". Multiplying both sides of Equation 1 by "x" and both sides of Equation 2 by "y", we get:
x * tan(47°) = d
y * tan(40°) = d
Solving for "x" and "y", we get:
x = d / tan(47°)
y = d / tan(40°)
Substituting the values of the angles given in the problem, we get:
x ≈ 17.04 meters
y ≈ 22.35 meters