Answer :
Answer:
The distance between the yacht from the ship is about 33.6 km.
Step-by-step explanation:
The diagram is attached below.
Point A is the shipe, Point B is the tugboat, and Point C is the yacht.
Since the tugboat is 28 km away, and the scale being used is 1 cm : 4 km, the tugboat is 7 cm away from the ship at a 210° bearing on the diagram.
Likewise, the yacht is 6 cm away from the tugboat at a 210° bearing.
To find the distance between the yacht to the ship, we need to
yacht to the ship, we need to determine the value of x.
To do so, we can use the Law of Cosines:
b²a² + c²2ac cos(B) =
First, we need to determine ZB.
A has a bearing of 210°. 180° is covered by QI and IV. So, the small angle in QIII is 30°.
By Alternate Interior Angles, the angle in QI (inside the triangle) of Point B must also be 30°.
And since Point B has a bearing of 310°, 270° is covered in total by QI, QIV, and QIII. So, 40° is left in QII.
Therefore, 50° is the measure of the angle in QIII within the triangle of Point B.
Thus, ZB measures 50° + 30° = 80°.
So, ZB measures 80°. We also know that a = 6 and c= 7. Substitute:
b² = (6)² + (7)² - 2(6)(7) cos(80)
Simplify and take the square root of both sides. So:
b = √85-84 cos(80)
Approximate using a calculator:
b = 8.3912... ≈ 8.39 cm
Since 1 cm: 4km, to find the distance in km, we simply need to multiply by four. So:
⇒b= 4(8.3912...) = 33.5651 ≈
33.6 km
The distance between the yacht from the ship is about 33.6 km.
Step-by-step explanation:
hope it helps you itz admirer
The distance of the yacht from the ship will be 33.6km.
How to calculate the distance?
From the information given, the tugboat is 28 km away at a bearing of 210°, and a yacht is 24 km from the tugboat at a bearing of 310°.
In this case, we can use the law of cosine formula to solve it and it will be:
b²= a² + c²2ac cos(B)
b² = 6² + 7² - (2 × 6 × 7)cos80°
b = 8.39
Therefore, since a scale of 1 cm : 4 km is used, the distance will be:
= 4 × 8.39
= 33.6km
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