Q,R,S are 3 point on the same horizontal plane,|QR| is equal 20m and |QS| is equal 32m the bearing of R and S from Q are 0.30° and 135° respectively.How far east of R is S
placing the angles in standard position, you need to find
32cos(-45°) - 20cos60° = 32 * 1/√2 - 20 * 1/2 = ____
To find the distance east of point R to point S, we need to use trigonometry and the given information.
First, let's draw a diagram to visualize the scenario:
Q-------------------------R-------------S
Considering the bearings given, we can determine the angles between the sides QR and QS with the horizontal plane:
Angle QRQ = 0.30°
Angle QSQ = 135°
Now, let's calculate the distance east of R to S.
Step 1: Determine the angle between the sides QR and QS:
Angle QRS = 180° - Angle QRQ - Angle QSQ
Angle QRS = 180° - 0.30° - 135°
= 44.70°
Step 2: Use trigonometry to determine the distance east of R to S:
We know that QR = 20m and QS = 32m.
We can use the sine function to relate the angle and the side opposite to it.
sin(angle) = opposite/hypotenuse
sin(QRS) = Distance east of R to S / QS
Rearranging the formula:
Distance east of R to S = sin(QRS) * QS
Distance east of R to S = sin(44.70°) * 32m
≈ 23.86m
Therefore, the distance east of point R to point S is approximately 23.86 meters.
To find how far east of point R the point S is located, we need to determine the distance between R and S in the eastward direction.
First, let's calculate the distances in the northward and eastward directions separately, using the given angles and distances.
1. Northward distance:
The bearing of R from Q is 0.30°, which means that R is 0.30° north of Q. Since the north direction is assumed to be positive, we have a positive displacement in the northward direction.
To calculate the northward displacement between R and Q, we can use trigonometry. Since the distance between Q and R is given as 20 meters, the northward displacement can be calculated as follows:
Northward displacement (NR) = |QR| * sin(bearing of R)
= 20 * sin(0.30°)
≈ 0.10 meters (rounded to two decimal places)
2. Eastward distance:
The bearing of S from Q is 135°, which means that S is 135° east of the north direction. Since the east direction is also assumed to be positive, we have a positive displacement in the eastward direction.
To calculate the eastward displacement between S and Q, we can use trigonometry as well. Since the distance between Q and S is given as 32 meters, the eastward displacement can be calculated as follows:
Eastward displacement (SQ) = |QS| * cos(bearing of S)
= 32 * cos(135°)
≈ -22.63 meters (rounded to two decimal places)
Note: The negative sign in front of 22.63 meters indicates that the displacement is in the opposite direction to the east, which is west.
Now, to find how far east of R the point S is located, we need to subtract the eastward displacement between R and S from the eastward displacement between S and Q, as they fall on the same horizontal plane:
Eastward distance between R and S = Eastward displacement (SQ) - Eastward displacement (SR)
Since SR is the eastward displacement between R and Q, which is assumed to be 0, we have:
Eastward distance between R and S = Eastward displacement (SQ) - 0
≈ -22.63 meters (rounded to two decimal places)
Therefore, point S is approximately 22.63 meters west of point R on the same horizontal plane.