Question

Two scuba divers are 30m apart below the surface of the water. They both spot a shark that is below them. The angle of depression from diver 1 to the shark is 52° and the angle of depression from diver 2 to the shark is 39°. How far is DIVER 1 from the shark?

Answer 1

Answer:

distance of diver 1 from the shark ≈ 18.88 m

Step-by-step explanation:

The illustration forms a triangle. The base of the triangle which is their distance apart is given as 30 m . The known angle of the triangle are 52° and 39°. To find the unknown side we subtract the sum of 52° and 39° from 180°. Note that the total angle in a triangle is 180°.

Therefore,

180 - (52 + 39) = 180 - 91  = 89 °. Now the three angle of the triangles are 52°, 39° and 89°.

Using the law of sine we can find the distance of the diver 1 from the shark.

let a = distance of the first diver to the shark.

a/sin 39° = 30/sin 89°

cross multiply

a sin 89° = 30 sin 39°

divide both sides by sin 89°

a = 30 sin 39°/sin 89°

a = 30 × 0.62932039105 /sin 89°

a = 18.8796117315 /0.99984769515

a = 18.8824876258

a ≈ 18.88 m