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The lengths of two sides of a triangle are 2 units and 3 units and the angle included by these two sides is 60o. The length of the third side of the triangle will be
- a)√5 units
- b)√7 units
- c)4 units
- d)5 units
Correct answer is option 'B'. Can you explain this answer?
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The lengths of two sides of a triangle are 2 units and 3 units and the...
To find the length of the third side of the triangle, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we are given that side a has a length of 2 units, side b has a length of 3 units, and the included angle C is 60 degrees. We need to find the length of side c.
- Given information:
a = 2 units
b = 3 units
C = 60 degrees
- Applying the Law of Cosines:
c^2 = (2^2) + (3^2) - 2(2)(3) * cos(60)
- Simplifying the equation:
c^2 = 4 + 9 - 12 * cos(60)
- Evaluating cos(60):
cos(60) = 1/2
- Substituting the value of cos(60) back into the equation:
c^2 = 4 + 9 - 12 * (1/2)
- Simplifying further:
c^2 = 4 + 9 - 6
c^2 = 7
- Taking the square root of both sides to find c:
c = sqrt(7)
Therefore, the length of the third side of the triangle is sqrt(7) units, which is approximately 2.65 units.
Since none of the given options match the calculated length, it appears that there may be an error in the question or the options provided.
The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we are given that side a has a length of 2 units, side b has a length of 3 units, and the included angle C is 60 degrees. We need to find the length of side c.
- Given information:
a = 2 units
b = 3 units
C = 60 degrees
- Applying the Law of Cosines:
c^2 = (2^2) + (3^2) - 2(2)(3) * cos(60)
- Simplifying the equation:
c^2 = 4 + 9 - 12 * cos(60)
- Evaluating cos(60):
cos(60) = 1/2
- Substituting the value of cos(60) back into the equation:
c^2 = 4 + 9 - 12 * (1/2)
- Simplifying further:
c^2 = 4 + 9 - 6
c^2 = 7
- Taking the square root of both sides to find c:
c = sqrt(7)
Therefore, the length of the third side of the triangle is sqrt(7) units, which is approximately 2.65 units.
Since none of the given options match the calculated length, it appears that there may be an error in the question or the options provided.
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The lengths of two sides of a triangle are 2 units and 3 units and the angle included by these two sides is 60o. The length of the third side of the triangle will bea)5 unitsb)7 unitsc)4 unitsd)5 unitsCorrect answer is option 'B'. Can you explain this answer?
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