Question

a canoe is seen floating down a creek. the canoe is first spotted 65 ft away. 7 seconds later the canoe is 40. ft away, making a 50° angle between the two settings how far did the canoe travel

Answer 1

To determine how far the canoe traveled, we can use trigonometry. Using the tangent function, we can find the distance the canoe traveled by setting up an equation and solving for x. The canoe traveled approximately 52.36 ft.

Step-by-step explanation:

To determine how far the canoe traveled, we can use trigonometry.

Let's call the distance the canoe traveled as x.

We have a right triangle formed by the distance the canoe was first spotted (65 ft), the distance the canoe was spotted 7 seconds later (40 ft), and the angle between the two sightings (50°).

Using the trigonometric function tangent (tan), we can set up the equation:

tan(50°) = (65 - x) / 40

Simplifying the equation, we get:

x = 65 - 40 * tan(50°)

Now we can calculate the value of x using a calculator:

x ≈ 52.36 ft

Therefore, the canoe traveled approximately 52.36 ft.

Answer 2

The canoe traveled approximately a distance of 21.9ft.

let the distance the canoe travels be "d".

Initial position = 65 ft

After 7s,

The Final position is 40ft away

From the given information the canoe moves =(65-40)=25ft closer

Let x=25ft

Using the tangent function

we know that, tan(50degree)=x/d

therefore, d=25/tan(50 degree)

d=21.9ft

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