Question

The look out point of a lighthouse is 30 feet above sea level. A boat is 20 feet away from the base of the lighthouse. What is the angle of depression from the look out point to the boat in the water? Round the answer to the nearest degree.
a.34B.42C.48D.56

Answer 1

Call the angles of depression D.

then tan(D)=20/30, or I

arctan(tan(D)) = arctan(⅔)

D=33.690. A is the answer

your calculator probably uses tan^-1 rather than arctan

Answer 2

Answer:

D. $56^{\circ}$

Step-by-step explanation:

Please find the attachment.

Let x be the angle of depression.

We have been given that the look out point of a lighthouse is 30 feet above sea level. A boat is 20 feet away from the base of the lighthouse.

Upon looking at our attachment we can see that the lighthouse and boat forms a right triangle with respect to sea level.

We will use tangent to solve for the angle of depression as tangent relates the opposite side of a right triangle with adjacent.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(x)=\frac{30}{20}$

$\text{tan}(x)=\frac{3}{2}$

Using arctan we will get,

$x=\text{tan}^{-1}(\frac{3}{2})$

$x=56.30993^{\circ}\approx 56^{\circ}$

Therefore, the angle of depression fro the look out point to the boat in the water is 56 degrees and option D is the correct choice.