A submersible traveling at a depth of 250 feet dives at an angle of 15º with respect to a line parallel to the water’s surface. It travels a horizontal distance of 1500 feet during the dive. What is the depth of the submersible after the dive?
Always make a sketch.
draw a horizontal showing 250 ft below the water line
mark it as 1500
draw a vertical at the end of the horizontal to show the depth of the dive, label it x
label the angle of the dive as 15°
Now, in relation to the Ø, isn't the horizontal line of 1500 the "adjacent" ?
and isn't he vertical line of x the "opposite"
Which trig ratio uses "adjacent" and "opposite"
(You must memorize the 3 main trig ratios !!!)
Did you picke:
tan15° = x/1500
x = 1500tan15°
= appr 401.9 ft
but the sub was already 250 ft deep, so the new depth is 651.9 ft
To find the depth of the submersible after the dive, we can use trigonometry.
Let's first draw a diagram to represent the situation.
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________/____|_________
1500 ft
In this diagram, the line parallel to the water's surface is represented by the horizontal line at the top. The submersible is represented by the line that forms a 15-degree angle with the horizontal line, and the depth of the submersible is represented by the line that goes straight down from the submersible.
Now, let's break down the problem.
The given information is:
- The submersible dives at an angle of 15 degrees.
- It travels a horizontal distance of 1500 feet.
We need to find the depth of the submersible.
To find the depth, we can use the trigonometric function tangent (tan).
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the opposite side is the depth of the submersible, and the adjacent side is the horizontal distance traveled.
So we can write the following equation:
tan(15 degrees) = depth / 1500
Now, we can solve for the depth by rearranging the equation:
depth = 1500 * tan(15 degrees)
Using a calculator, we can find the value of tan(15 degrees) to be approximately 0.2679.
Plugging in this value into the equation, we get:
depth = 1500 * 0.2679
Calculating this, we find that the depth of the submersible after the dive is approximately 401.85 feet.
Therefore, the depth of the submersible after the dive is approximately 401.85 feet.
To find the depth of the submersible after the dive, we can first determine the vertical distance it travels during the dive.
Since the submersible is diving at an angle of 15º, we can use trigonometry to find the vertical distance. The vertical distance can be calculated by multiplying the horizontal distance traveled by the tangent of the angle.
Tangent of the angle = Opposite / Adjacent
In this case, the angle is 15º, and the horizontal distance traveled is 1500 feet. Let's calculate the vertical distance:
Vertical distance = Horizontal distance * Tangent(angle)
Vertical distance = 1500 feet * tan(15º)
Vertical distance ≈ 392.7 feet
So, the vertical distance the submersible travels during the dive is approximately 392.7 feet.
Now, to find the depth of the submersible after the dive, we need to add this vertical distance to the initial depth of 250 feet.
Depth after dive = Initial depth + Vertical distance
Depth after dive = 250 feet + 392.7 feet
Depth after dive ≈ 642.7 feet
Therefore, the depth of the submersible after the dive is approximately 642.7 feet.