What is the Resultant Force of Tensions in Two Fishing Lines?

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To find the resultant force of tensions in two fishing lines with tensions of 20N and 30N at a 30-degree angle, the cosine rule is applied. The triangle of forces is set up with sides representing the tensions and the angle between them. The calculation yields a resultant force expression of 10√(6√3 + 13). However, the expected answer is given as 10√7, leading to confusion regarding the discrepancy. The discussion emphasizes the importance of correctly applying the cosine rule to resolve the resultant force accurately.
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Homework Statement


Two fishing lines hook onto one fish. The tensions in the lines are 20N and 30N, the angle between them being 30 degrees. Use a triangle of forces to find the magnitude of the resultant force of the tensions.


Homework Equations


cosine rule a^2 = b^2 +c^2 -2cbcos(theta)


The Attempt at a Solution



Triangle gives b=20, c = 30 and theta = 150.

Solving Resultant = 10root(6root(3) +13)


ANSWER IS GIVEN AS 10root(7), don't know how they get to this.
 
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dan2xtermart said:
Solving Resultant = 10root(6root(3) +13)
Your answer is correct.
 

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