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ataglance05
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A triangle has an angle A=35 degrees and an angle B=40 degress and side a=3680 meters. What are the lengths of sides b&c?
The formula for finding the length of side b in a triangle is: b = a * sin(B) / sin(A), where a is the length of side a, A is the angle opposite to side a, and B is the angle opposite to side b.
The Law of Cosines states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the included angle. This can be written as: c^2 = a^2 + b^2 - 2ab * cos(C), where c is the length of side c and C is the angle opposite to side c. This formula can be rearranged to solve for c, allowing us to find the length of side c when given two sides and the included angle.
There can be one, two, or no solutions when finding the length of side b in a triangle. If the given angles and side a do not satisfy the triangle inequality theorem, there will be no solutions. If there is one solution, it is known as the unique solution. If there are two solutions, it is known as the ambiguous case, and we must use the Law of Cosines to determine which solution is the correct one.
Yes, you can use the same formula to find the length of side c in a triangle when given two angles and side b. However, you will need to rearrange the formula to solve for c, as the original formula is for finding the length of side b. The rearranged formula will be: c = b * sin(C) / sin(B), where b is the length of side b, B is the angle opposite to side b, and C is the angle opposite to side c.
No, it is not possible to find the length of all three sides of a triangle when given only two angles. This is because the length of a triangle's sides is dependent on the size of its angles and the triangle's shape. Without knowing the length of at least one side, we cannot determine the lengths of the other sides.