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Brilliant_brown [7]
3 years ago
10

Isaac is looking through binoculars on a whale watching trip when he notices a sea otter in the distance. If he is 20 feet above

sea level in the boat, and the angle of depression is 30 degrees, how far away from the boat is the otter (to the nearest foot)?

Mathematics
2 answers:
sveta [45]3 years ago
6 0
Tan of an angle = perpendicular / base 
<span>Here, perpendicular is the side of the triangle opposite the angle. </span>
<span>And base is the arm of the angle other the hypotenuse. </span>

<span>If the side of the triangle to be found (marked as ? in the figure) is x, then </span>

<span>perpendicular = 20 feet </span>
<span>base = x </span>

<span>so, tan 30 = 20/x </span>
<span>so, x = 20/(tan 30 degrees) = 34.64 feet </span>
<span>= 35 feet to the nearest foot</span>
Alex777 [14]3 years ago
3 0

Answer:

<h2>The otter is 34 feet from the boat, approximately.</h2>

Step-by-step explanation:

The angle of depression is the angle formed by the horizontal and the line of sight. The image attached shows an example.

Now, as you can observe, the situation can be modeled by a right triangle, where we need to use trigonometric reasons to find the answer, the horizontal distance.

tan30=\frac{y}{x}=\frac{20}{x} \\ x=\frac{20}{tan30} =\frac{20}{0.58}\\ x \approx 34

Therefore, the otter is 34 feet from the boat, approximately.

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