Question

solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 1. . a = 5, b = 7, C = 42° 2. . a = 10, b = 3, C = 15° 3. b = 5,c = 3, A = 102° 4. . b = 4c = 1, A = 100° 5. . a = 6, c = 5, B = 50° = 55° 15. a = 5.c = 2. B = 90° 5, B = 90° = 7. c = 10 17. a = 5, b

Answer 1

To solve triangles, we use various methods depending on the known elements of the triangle, such as the Pythagorean theorem for right triangles and the Law of Sines or Law of Cosines for other triangles.

Step-by-step explanation:

To solve a triangle means to find the unknown side lengths and angle measures given some known values. This is often done using the Law of Sines or Law of Cosines in non-right triangles, or the Pythagorean theorem and trigonometric ratios in right triangles. For example, in a right triangle where we are given two side lengths, we can use the Pythagorean theorem to find the third side: a² + b² = c². If we only have one side and one angle, we can use trigonometric ratios such as sine, cosine, or tangent to find the remaining sides and angles.

For the specific example where we have side a = 5, side b = 7, and angle C = 42°, we can use the Law of Cosines to find the length of side c. Then, we can use the Law of Sines or use the sum of angles in a triangle to find the other angles.

For the more complex situations where the combination of given sides and angles does not immediately suggest a specific formula, we must analyze the triangle's information to decide on the appropriate method to solve it.