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andrew-mc [135]
3 years ago
8

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 t

he 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

Mathematics
2 answers:
olya-2409 [2.1K]3 years ago
8 0
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
s2008m [1.1K]3 years ago
3 0

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.

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