Question
A ship is on the surface of the water,
and its radar detects a submarine
238 feet away, at an angle of
depression of
underwater is the submarine?
a) 93 feet
b) 219 feet
c) 42 feet
d) 101 feet
e) 209 feet
and its radar detects a submarine
238 feet away, at an angle of
depression of
underwater is the submarine?
a) 93 feet
b) 219 feet
c) 42 feet
d) 101 feet
e) 209 feet
Ask by Malone Lambert. in the United States
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The submarine is 93 feet underwater.
Answer:
a) 93 feet
Answer:
a) 93 feet
Solution
To determine the depth of the submarine, we can use trigonometry, specifically the sine function in a right triangle.
Given:
- Distance (hypotenuse) from the ship to the submarine: 238 feet
- Angle of depression:
Objective:
Find the depth (
Find the depth (
Approach:
-
Understand the Scenario:
- The angle of depression is measured from the horizontal line of sight downward to the submarine.
- This forms a right triangle where:
- The hypotenuse is the line of sight (238 feet).
- The opposite side is the depth of the submarine (
). - The adjacent side is the horizontal distance from the ship to the point directly above the submarine.
-
Use the Sine Function:
-
Solve for Depth (
): -
Calculate
: -
Compute the Depth:
Answer:
a) 93 feet
a) 93 feet
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To find the depth of the submarine, we can use the trigonometric relationship involving the angle of depression. The angle of depression is the angle from the horizontal line down to the line of sight to the submarine. In this case, we can imagine a right triangle where the distance from the ship to the submarine on the surface is the base (238 feet) and the depth of the submarine is the opposite side.
Using the tangent function, we know that:
To find the depth:
Calculating this gives:
So, the correct answer is (a) 93 feet! It’s always a splash of fun to see how math can help us uncover mysteries beneath the waves!
Now imagine this: if submarines can just dip beneath the surface undetected by ships, think of all the sneaky missions they could be on! From covert military operations to deep-sea explorations, the underwater world is a realm of adventure and science!
