Angle Side Theorem Calculator

Angle Side Theorem (Law of Sines):

\[ \text{Side} = \text{opposite\_side} \times \frac{\sin(\text{angle})}{\sin(\text{opposite\_angle})} \]

Calculated Side:

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1. What is the Angle Side Theorem?

The Angle Side Theorem, also known as the Law of Sines, relates the lengths of sides of a triangle to the sines of its opposite angles. It's particularly useful for solving triangles when you know two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

2. How Does the Calculator Work?

The calculator uses the Law of Sines formula:

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

Where:

\( a, b, c \) — Sides of the triangle
\( A, B, C \) — Angles opposite to sides a, b, c respectively

Explanation: The calculator rearranges the formula to solve for an unknown side when you know one side and two angles.

3. Importance of the Angle Side Theorem

Details: This theorem is fundamental in trigonometry and has applications in navigation, surveying, physics, and engineering. It allows calculation of unknown sides or angles in non-right triangles.

4. Using the Calculator

Tips: Enter the known side length, its opposite angle, and another angle whose opposite side you want to find. All angles must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: When can't the Law of Sines be used?
A: It can't be used for right triangles (use Pythagorean theorem instead) or when you only know three sides (SSS) or two sides and their included angle (SAS).

Q2: What is the ambiguous case?
A: When solving SSA triangles, there might be two possible solutions, one solution, or no solution depending on the values.

Q3: Does this work for any triangle?
A: Yes, the Law of Sines works for all triangles - acute, right, and obtuse.

Q4: What units should I use for angles?
A: The calculator uses degrees. If you have radians, convert them to degrees first.

Q5: How accurate are the results?
A: Results are accurate to 4 decimal places, but remember that real-world measurements have their own precision limits.