When given three angles and one side, what method is used to find other sides?

When given three angles and one side, what method is used to find other sides?

• A. Law of cosines
• B. Law of sines
• C. Geometric progression
• D. Trigonometric identities

Answer: (B)

To determine the lengths of the other sides of a triangle when provided with three angles and one side, the Law of Sines is the appropriate method to use. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle. This relationship can be expressed mathematically as: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] where \(a\), \(b\), and \(c\) are the lengths of the sides of the triangle, and \(A\), \(B\), and \(C\) are the angles opposite those sides, respectively. Given three angles (which inherently sum to 180 degrees in a triangle), you can easily calculate the sine values for each angle. With the known side length corresponding to one of the angles, you can set up the ratios to solve for the lengths of the other sides. The other choices provided do not fit this scenario: - The Law of Cosines is more appropriate when dealing with two sides and the included angle, rather than three angles and one side. - Ge

To determine the lengths of the other sides of a triangle when provided with three angles and one side, the Law of Sines is the appropriate method to use. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle. This relationship can be expressed mathematically as:

[

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

]

where (a), (b), and (c) are the lengths of the sides of the triangle, and (A), (B), and (C) are the angles opposite those sides, respectively.

Given three angles (which inherently sum to 180 degrees in a triangle), you can easily calculate the sine values for each angle. With the known side length corresponding to one of the angles, you can set up the ratios to solve for the lengths of the other sides.

The other choices provided do not fit this scenario:

• The Law of Cosines is more appropriate when dealing with two sides and the included angle, rather than three angles and one side.

• Ge