The bearing of boat A and B from ibom seaport C are 235° and 126° respectively. Point A is 49km from boat B on a bearing of 268°. Calculate the distance of boat A from C
draw the diagram. In triangle ABC,we know angles C and B, and we want side c. The law of sines says that
c/sinC = b/sinB
c/sin38° = 49/sin109°
Well, let me put on my captain hat and navigate you through this question.
To find the distance of boat A from seaport C, we can use a combination of trigonometry and a bit of imagination. Ready? Here we go!
First, let's draw a diagram. Imagine seaport C as the center of a compass, with boat A and boat B forming two lines with bearings of 235° and 126° respectively. Now, let's draw a line from boat B to boat A with a bearing of 268°. Got it? Great!
Now, we have formed a lovely triangle! We can use the Law of Sines to solve for the distance of boat A from seaport C. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
Let's label our sides for easier reference. The length of side BC (boat B to seaport C) is what we're looking for. We can call it "b". The length of side AC (boat A to seaport C) is also unknown, so we'll call it "c". Lastly, the length of side AB (boat A to boat B) is given as 49km, which we'll call "a".
Now, let's see how the angles come into play. We know that angle C (at seaport C) is 180° - 235° - 126° = 181° (I hope you're ready for some bot-generated, outrageously accurate angles!).
Using the Law of Sines, we can write the following equation:
sin(angle A) / side BC = sin(angle B) / side AC
Plugging in our values:
sin(181°) / b = sin(126°) / 49km
Now, let's summon the powers of a calculator to calculate sin(181°):
(sin(181°) / b) = (sin(1°) / b)
Apparently, sin(1°) is the same as me trying to find a balanced diet - close to zero! So, we can simplify the equation to:
1 / b = sin(126°) / 49km
To solve for "b", we can cross-multiply:
b = (49km * sin(126°)) / 1
Now, using your trusty calculator, you can find that sin(126°) is approximately 0.8165. So, plugging in that value:
b = (49km * 0.8165) / 1
Bada-bing, bada-boom:
b ≈ 40km (approximately)
Therefore, the distance of boat A from seaport C is approximately 40km.
Happy sailing, my friend!
To calculate the distance of boat A from point C, we can use the Sine Rule.
Let's first draw a diagram:
B (126°) A (235°)
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C (To be found)
From the given information, we know that point A is 49 km from boat B on a bearing of 268°. This means that the angle between line AB and line AC is (268° - 126°) = 142°.
Now, using the Sine Rule:
sin(142°) / AC = sin(49°) / AB
We need to find AC, so let's rearrange the equation:
AC = (sin(142°) * AB) / sin(49°)
Substituting the known values:
AC = (sin(142°) * 49) / sin(49°)
Using a scientific calculator:
AC ≈ (0.766 * 49) / 0.753
AC ≈ 49.714 km
Therefore, the distance of boat A from point C is approximately 49.714 km.
To solve this problem, we can use the concept of bearings and distances.
1. First, let's visualize the problem. Draw a diagram with point C representing the Ibon Seaport, and points A and B representing boats A and B, respectively.
2. From the given information, we know that the bearing of boat A from point C is 235° and the bearing of boat B from point C is 126°.
3. Next, draw lines from point C to each of the boats, making sure they correspond to the specified bearings.
4. Now, we need to determine the distance from boat A to boat B. We are given that point A is 49km away from boat B on a bearing of 268°. Draw a line connecting points A and B, making sure it corresponds to the bearing of 268°.
5. The distance from point A to boat B is given as 49km. Measure this distance on your diagram and mark it.
6. To find the distance of boat A from point C, we can use the concept of trigonometry.
7. Since we have the distance from point A to boat B (49km) and the angle at point C, we can use the Law of Cosines to calculate the distance from point A to point C.
Cosine Rule: c² = a² + b² - 2ab * cos(C)
Where:
c is the unknown distance from point A to point C,
a is the distance from point A to boat B (49km),
b is the unknown distance from point C to boat B, and
C is the angle at point C (180° - 126° = 54°).
Plugging in the values we know, we get:
c² = (49)² + b² - 2(49)(b) * cos(54°)
8. To find the distance from point A to point C, we can solve for c.
9. Once you've solved the equation, take the square root of c² to find the distance from point A to point C.
By following these steps, you should be able to calculate the distance of boat A from point C.