From the hay loft door, Ted sees his dog on the ground. The angle of depression to the dog is 40º. Ted's eye level is 16 feet above the ground. How many feet must the dog walk to reach the open barn door directly below Ted (to the nearest foot)?

Where α is the angle of depression of the dog, the opposite side (16) is Ted's eye level above the ground, and the adjacent side (x) is the distance between the dog and the barn door.

Replacing with the values given:

tan40 = 16/x

Solving for x

x =16/tan40

x= 19 ft

Feel free to ask for more if needed or if you did not understand something.

ShiaLabeouf ShiaLabeouf · Answer 2 · 2024-10-25T21:26:24-04:00

Final answer:

To find the distance the dog must walk to reach the open barn door directly below Ted, we can use the concept of trigonometry and the angle of depression. By setting up and solving the equation using the tangent function, we can determine the distance in feet.

Explanation:

To find the distance the dog must walk to reach the open barn door, we need to use the concept of trigonometry and the angle of depression. Since the angle of depression is 40° and Ted's eye level is 16 feet above the ground, we can use the tangent function to calculate the distance. The tangent of an angle is equal to the opposite side divided by the adjacent side.

Let's define the distance the dog must walk as x. From the given information, we have the opposite side (Ted's eye level) as 16 feet and the angle of depression as 40°. Using the tangent function, we can set up the equation:

Tan(40°) = opposite / adjacent

Tan(40°) = 16 / x

Now, we can solve for x by multiplying both sides of the equation by x and dividing by Tan(40°). This gives us:

x = 16 / Tan(40°)

Using a calculator, we can find the approximate value of x to the nearest foot.

Learn more about Trigonometry here:

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