122k views
3 votes
A sensor on a boat notices buried treasure 200 meters away diagonally with an angle of depression of 25 degrees. How deep is the treasure beneath the water rounded to the nearest tenth of a meter?

1 Answer

4 votes

Answer: To solve this problem, we can use the Pythagorean theorem. Let's call the depth of the treasure "d".

We can create a right triangle with the following sides:

The sensor on the boat is at the top of the triangle and is 200 meters away from the treasure diagonally.

The line from the sensor to the treasure, which we can call "x", is at a 25-degree angle from the surface of the water.

The line from the treasure to the ocean floor, which we can call "d", is perpendicular to the surface of the water.

Since we know that the angle of depression is 25 degrees, we can use tangent to find the length of x.

tan(25) = x/d

x = d * tan(25)

Now, we have two sides of a right triangle and can use the Pythagorean theorem to find d:

x^2 + d^2 = 200^2

d^2 = 200^2 - x^2

d^2 = 200^2 - (d * tan(25))^2

Solving for d, we find that d = 174.59 meters. Rounding to the nearest tenth of a meter, we get d = 174.6 meters.

Explanation:

User General Mac
by
7.7k points