A scuba diver is 356 feet below the surface of the water. The angle of depres- sion the diver makes with her boat is 39°. Draw a diagram that you can use to determine how far the diver is from the boat.
A scuba diver is 356 feet below the surface of the water. The angle of depres- sion the diver makes with her boat is 39°. Draw a diagram that you can use to determine how far the diver is from the boat.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section: Chapter Questions
Problem 40CT: To determine the angle of elevation of a star in the sky, you align the star and the top of the...
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![**Problem Statement**
A scuba diver is 356 feet below the surface of the water. The angle of depression the diver makes with her boat is 39°.
**Instructions**
Draw a diagram that you can use to determine how far the diver is from the boat.
**Diagram Explanation**
To solve this problem, you need to draw a right triangle:
1. **Vertical Line (Opposite Side)**: Represent the depth of the water from the surface to the diver, which is 356 feet.
2. **Horizontal Line (Adjacent Side)**: This line will connect the point directly above the diver (at the water's surface) horizontally to the point where the boat is floating.
3. **Hypotenuse**: This will be the line from the diver to the boat, which we want to find.
Place the angle of depression, 39°, at the intersection of the surface line and the hypotenuse (Angle with the surface line).
By using trigonometric relationships, specifically the tangent function (tan), you can solve for the distance from the diver to the boat. The tangent of the angle of depression (39°) is equal to the opposite side (depth of 356 feet) divided by the adjacent side (horizontal distance from the point above the diver to the boat).
\[ \tan(39^\circ) = \frac{\text{opposite}}{\text{adjacent}} \]
Rearranging to solve for the adjacent side:
\[ \text{adjacent} = \frac{\text{opposite}}{\tan(39^\circ)} \]
Finally, use the trigonometric relationships to solve for the hypotenuse to determine how far the diver is from the boat.
This diagram effectively visualizes the relationships and measurements needed to solve the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81d865ca-ed2c-4f6d-a4cc-7f843242dec1%2F6e7785e6-ffee-477f-8dc2-cb508e2f295d%2Fyff0osa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
A scuba diver is 356 feet below the surface of the water. The angle of depression the diver makes with her boat is 39°.
**Instructions**
Draw a diagram that you can use to determine how far the diver is from the boat.
**Diagram Explanation**
To solve this problem, you need to draw a right triangle:
1. **Vertical Line (Opposite Side)**: Represent the depth of the water from the surface to the diver, which is 356 feet.
2. **Horizontal Line (Adjacent Side)**: This line will connect the point directly above the diver (at the water's surface) horizontally to the point where the boat is floating.
3. **Hypotenuse**: This will be the line from the diver to the boat, which we want to find.
Place the angle of depression, 39°, at the intersection of the surface line and the hypotenuse (Angle with the surface line).
By using trigonometric relationships, specifically the tangent function (tan), you can solve for the distance from the diver to the boat. The tangent of the angle of depression (39°) is equal to the opposite side (depth of 356 feet) divided by the adjacent side (horizontal distance from the point above the diver to the boat).
\[ \tan(39^\circ) = \frac{\text{opposite}}{\text{adjacent}} \]
Rearranging to solve for the adjacent side:
\[ \text{adjacent} = \frac{\text{opposite}}{\tan(39^\circ)} \]
Finally, use the trigonometric relationships to solve for the hypotenuse to determine how far the diver is from the boat.
This diagram effectively visualizes the relationships and measurements needed to solve the problem.
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