Question

Two scuba divers, Jim and Tara, are 20m apart below the surface of the water. They both spot a shark that is below them. The angle of depression from Jim to the shark is 47 degrees, and the angle of depression from Tara to the shark is 40 degrees. How far is Jim from the shark?

Answer 1

Answer:

Jim is 12.87 meters away from the shark.

Step-by-step explanation:

We are given that,

Distance between Jim and Tara = 20 meters.

The angle of depression of the shark from Jim and Tara is 47° and 40° respectively as shown in the figure below.

So, the third angle of the triangle formed is given by,

47° + 40° + ∠S = 180°

i.e. ∠S = 180° - 87°

i.e. ∠S =93°

So, now using the sine ratio formula, we have,

$\frac{20}{\sin 93}=\frac{x}{\sin 40}$

i.e. $x=\frac{20\times 0.6428}{0.9986}$

i.e. $x=\frac{12.856}{0.9986}$

i.e. x = 12.87 meters

Thus, Jim is 12.87 meters away from the shark.