SOLUTION: The sonar of a navy cruiser, sailing on the surface of the ocean, detects a submarine that is 4000 feet (measured in a straight line distance) from the cruiser. The angle of depres

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Question 1203442: The sonar of a navy cruiser, sailing on the surface of the ocean, detects a submarine that is 4000 feet (measured in a straight line distance) from the cruiser. The angle of depression from the cruiser to the submarine is 31.2 °.
How deep is the submarine? Round to the nearest tenth.

What is its horizontal distance from the navy cruiser to the submarine? Round to the nearest tenth.
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Drawing and labeling the figure is not complicated. From there, you have simple trigonometry which should be easily interpreted.


for the horizontal distance h, hypotenuse straight line distance 4000, you have .

d, for how deep:
How DEEP is the submarine?
sin%2831.2%29=d%2F4000------------solve this to answer the question.
.
.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Draw out a right triangle with
  • horizontal leg = x
  • vertical leg = y
  • hypotenuse = 4000


sin(angle) = opposite/hypotenuse
sin(31.2) = y/4000
y = 4000*sin(31.2)
y = 2072.10803749252
y = 2072.1

cos(angle) = adjacent/hypotenuse
cos(31.2) = x/4000
x = 4000*cos(31.2)
x = 3421.45704064202
x = 3421.5


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Answers:

The submarine has a depth of approximately 2072.1 feet.

Horizontal distance = 3421.5 feet (approximate)