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By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
<h3>What is the direction and magnitude of the resulting displacement with respect to the origin</h3>
In this problem we assume that the <em>first</em> angle is measured with respect to the <em>east</em> side and that the <em>second</em> angle is <em>counterclockwise</em> and measured with respect to the direction of the <em>first</em> vector. First, we need to determine the resulting vector by using <em>trigonometric</em> and <em>vectorial</em> formulas:
(x, y) = (240 · cos 290°, 240 · sin 290°) + (50 · cos 320°, 50 · sin 320°)
(x, y) = (120.387, - 257.666) [mi]
The magnitude is found by Pythagorean theorem:
r ≈ 284.403 mi
The direction of the boat is obtained by <em>inverse trigonometric</em> functions:
θ = tan⁻¹ (- 257.666/120.387)
θ ≈ 295.043°
By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
To learn more on vectors: brainly.com/question/13322477
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