Question

Solve for all missing sides and angles in each triangle. Round to the nearest tenth.

A) Law of Cosines
B) Law of Sines
C) Pythagorean theorem
D) Special right triangles

Answer 1

To solve for missing sides and angles in triangles, you can use the Law of Cosines, Law of Sines, Pythagorean Theorem, or Special Right Triangles.

Step-by-step explanation:

The student is asking how to solve for missing sides and angles in triangles using different methods. Here are the steps for each:

1. Law of Cosines: Use this when you have two sides and the angle between them. Use the formula c^2 = a^2 + b^2 - 2ab(cosC) to solve for the remaining side or angle.
2. Law of Sines: Use this when you have an angle and the opposite side. Use the formula (sinA/a) = (sinB/b) = (sinC/c) to solve for the remaining sides and angles.
3. Pythagorean Theorem: Use this when you have a right triangle. Use the formula a^2 + b^2 = c^2 to solve for the missing side or angle.
4. Special Right Triangles: Use this when you have a special right triangle, such as a 45-45-90 or 30-60-90 triangle. Use the ratios of the sides (1:1:sqrt(2) for a 45-45-90 triangle and 1:sqrt(3):2 for a 30-60-90 triangle) to solve for the missing sides.