Question

about travels in the following path. How far north did it travel? Round your answer to the nearest 10th of a mile

Answer 1

The boat, with a reference angle of 23 degrees and an adjacent side of 45 miles, traveled approximately 19.1 miles north, determined using the tangent function.

Reference angle: 23 degrees

Adjacent side: 45 miles

Use the tangent function (TOA):

The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. The formula is given by:

Tangent(angle) = Opposite/Adjacent

Plugging in the values:

Tan(23 degrees) = x/45

Solve for the opposite side (x):

x = 45 * Tan(23 degrees)

Calculate the result:

Use a calculator to find the value of Tan(23 degrees) and then multiply it by 45:

x = 45 * Tan(23 degrees) ≈ 45 * 0.424474 ≈ 19.1

Therefore, x ≈ 19.1 miles (rounded to the nearest tenth of a mile).

So, the boat traveled approximately 19.1 miles north.

Answer 2

19.1 miles

Explanation:

The situation given represents a right triangle.

Thus, we would use trigonometric function to find how far north the boat travelled.

Let's represent how far the boat travelled north with "x".

Thus:

Reference angle = 23°

Opposite = x

Adjacent = 45 miles

Apply TOA:

Tan 23° = Opp/Adj

Tan 23° = x/45

Multiply both sides by 45

45 × Tan 23° = x

x = 45 × Tan 23°

x = 19.1013667

x = 19.1 miles (nearest tenth of a mile)