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StopLearn Team Staff answered 1 year ago To find the bearing and distance of point R from point Q, we can use the following steps:
- Draw a diagram: Draw a diagram that accurately represents the given information. Label points P, Q, and R, and mark the distances and directions between them.
- Find the distance between Q and R: To find the distance between Q and R, we can use the Pythagorean theorem. The distance between Q and R is the hypotenuse of a right triangle with legs of length 30 km (the distance between P and Q) and 40 km (the distance between Q and R).
Distance QR = √(30² + 40²) km Distance QR = √(900 + 1600) km Distance QR = √2500 km Distance QR = 50 km
Therefore, the distance between Q and R is 50 km.
- Find the bearing of R from Q: The bearing of R from Q is the direction of R with respect to Q, measured in degrees clockwise from due north. To find the bearing, we can use trigonometry.
Bearing of R from Q = θ = tan⁻¹(30/40)
θ = tan⁻¹(0.75)
θ = 36.87° (rounded to two decimal places)
Therefore, the bearing of R from Q is 36.87°.
Thus, we have found that the distance of R from Q is 50 km and the bearing of R from Q is 36.87°.
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