The bearings of ships A AND B from port p are 2.25 degree and 116 respectively.ship A is 3.9km from ship B on a bearing of 258 degree. Calculate the distance of ship A from p
To calculate the distance of ship A from port P, we can use the law of sines. Let's break down the problem into smaller steps.
Step 1: Draw a diagram
Draw a diagram with three points: port P, ship A, and ship B. Label the distance between ship A and ship B as 3.9 km and the angle between the bearing of ship B from port P and the direction from ship A to ship B as 258 degrees.
B
/
/ 3.9 km
/
P
\
\
\ A
Step 2: Determine the angle between the bearing of ship A from port P and the direction from ship A to ship B.
Since the bearing of ship A from port P is given as 2.25 degrees, and the bearing of ship B from port P is given as 116 degrees, we can find the angle between both bearings.
Angle between bearings = Bearing of ship A - Bearing of ship B
Angle between bearings = 2.25 degrees - 116 degrees
Angle between bearings = -113.75 degrees (Note: We obtained a negative angle because the bearings are in opposite directions.)
Step 3: Calculate the angle between ship A and port P using the angle between the bearings and the given angle between the bearing of ship B and the direction from ship A to ship B.
To calculate the angle between ship A and port P, we can subtract the angle between the bearings from the angle between the bearing of ship B and the direction from ship A to ship B.
Angle between ship A and port P = Angle between the bearing of ship B and the direction from ship A to ship B - Angle between bearings
Angle between ship A and port P = 258 degrees - (-113.75 degrees)
Angle between ship A and port P = 371.75 degrees
Step 4: Apply the law of sines to find the distance of ship A from port P.
The law of sines states that the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles of a triangle. In this case, we can relate the distance of ship A from port P to the angle between ship A and port P.
Using the law of sines:
Distance of ship A from port P / sin(116 degrees) = Distance of ship B from port P / sin(371.75 degrees)
Now, we rearrange the equation to solve for the distance of ship A from port P:
Distance of ship A from port P = (sin(116 degrees) / sin(371.75 degrees)) * Distance of ship B from port P
Plug in the values:
Distance of ship A from port P = (sin(116 degrees) / sin(371.75 degrees)) * 3.9 km
Using a scientific calculator, calculate the sine of 116 degrees and 371.75 degrees:
sin(116 degrees) ≈ 0.92978
sin(371.75 degrees) ≈ 0.66913
Substitute these values into the equation:
Distance of ship A from port P ≈ (0.92978 / 0.66913) * 3.9 km
Distance of ship A from port P ≈ 5.129 * 3.9 km
Distance of ship A from port P ≈ 20.0109 km
Therefore, ship A is approximately 20.0109 km from port P.
sorry i haven't see how to solve or please draw for me.
Trying to follow your description, but I am not able to sketch the diagram.
Given: PA = ___ [225o], PB = ___ [116o], AB = 3.9km[258o], PA = ?.
P = 180-45-26 = 109o.
B = 90-64-12 = 14o.
A = 180-109-14 = 57o.
PA/sin14 = 3.9/sin109
PA = 1 km.
PA = 1km[225o].
PB/sin57 = 3.9/sin109
PB = 3.5 km.
PB = 3.5 km[116o].