In the desert

A man wondering in the desert walks 5.7 miles in the direction S 26° W. He then turns 90° and walks 9 miles in the direction N 49° W. At that time, how far is he from his starting point, and what is his bearing from his starting point?

Correct answer:

m = 9.32 mi
φ = 274.8074 °

Step-by-step explanation:

a = 5.7 mi b = 9 mi α = 180 + 26 = 206^{\circ} β = 360 - 49 = 311^{\circ} x_{1} = a \cdot sin α = a \cdot sin 206 ° = 5.7 \cdot sin 206 ° = 5.7 \cdot (- 0.438371) = - 2.49872 mi y_{1} = a \cdot cos α = a \cdot cos 206 ° = 5.7 \cdot cos 206 ° = 5.7 \cdot (- 0.898794) = - 5.12313 mi x_{2} = b \cdot sin β = b \cdot sin 311 ° = 9 \cdot sin 311 ° = 9 \cdot (- 0.75471) = - 6.79239 mi y_{2} = b \cdot cos β = b \cdot cos 311 ° = 9 \cdot cos 311 ° = 9 \cdot 0.656059 = 5.90453 mi x = x_{1} + x_{2} = (- 2.4987) + (- 6.7924) ≐ - 9.2911 mi y = y_{1} + y_{2} = (- 5.1231) + 5.9045 ≐ 0.7814 mi m = x^{2} + y^{2} = (- 9.2911)^{2} + 0.781 4^{2} = 9.32 mi

tan φ = y : x x < 0; y > 0; \dots . I V . Q u a d r a n t Φ = \frac{1 8 0 °}{π} \cdot arctan (∣ y ∣ / ∣ x ∣) = \frac{1 8 0 °}{π} \cdot arctan (∣ 0.7814 ∣ / ∣ (- 9.2911) ∣) ≐ 4.8074^{\circ} φ = 270 + Φ = 270 + 4.8074 = 274.807 4^{\circ} = 274 ° 4 8^{'} 27 "

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators

Do you want to convert length units?
See also our right triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:

We encourage you to watch this tutorial video on this math problem: video1 video2 video3