Triangle Solver: Step-by-Step Guide

Introduction to Triangle Solver

The Triangle Solver is a powerful tool used to find the missing sides and angles of a triangle given three known values. In this guide, we will walk you through the steps to solve a triangle manually.

Formula and Variable Legend

The formula used to solve a triangle is the Law of Cosines, which states: c² = a² + b² - 2ab * cos(C) where a, b, and c are the sides of the triangle, and C is the angle opposite side c.

Diagram

Imagine a triangle with sides a, b, and c, and angles A, B, and C.

Step-by-Step Guide

Step 1: Gather Your Inputs

First, identify the three known values of the triangle. These can be any combination of sides (a, b, c) and angles (A, B, C).

Step 2: Determine the Type of Triangle

Next, determine the type of triangle you are dealing with. If you know two sides and the included angle, you can use the Law of Cosines to find the third side. If you know two angles and the included side, you can use the Law of Sines to find the other sides.

Step 3: Apply the Formula

Now, plug in the values you know into the formula. For example, if you know sides a and b, and angle C, you can use the Law of Cosines to find side c: c² = a² + b² - 2ab * cos(C)

Step 4: Solve for the Unknown

Solve for the unknown value using the formula. For example, if you are solving for side c, take the square root of both sides: c = √(a² + b² - 2ab * cos(C))

Step 5: Find the Remaining Sides and Angles

Once you have found one unknown value, you can use it to find the remaining sides and angles. For example, if you know two sides and the included angle, you can use the Law of Sines to find the other angles.

Step 6: Check Your Work

Finally, check your work by plugging your answers back into the original formula. This will help you catch any mistakes and ensure that your solution is correct.

Worked Example

Suppose we know sides a = 3 and b = 4, and angle C = 60°. We can use the Law of Cosines to find side c: c² = 3² + 4² - 234 * cos(60°) c² = 9 + 16 - 24 * 0.5 c² = 25 - 12 c² = 13 c = √13

Common Mistakes to Avoid

• Forgetting to square the sides when using the Law of Cosines
• Using the wrong formula for the type of triangle you are dealing with
• Not checking your work to catch mistakes

When to Use a Calculator

While it is possible to solve a triangle manually, it can be time-consuming and prone to errors. If you need to solve many triangles or want to check your work quickly, it is convenient to use a calculator or computer program to do the calculations for you.