Pre-Calculus Prep: Law of Sines - Finding the Missing ANGLE of a Non-Right Triangle

In pre-calculus, the Law of Sines is a trigonometric tool used to solve triangles that are not right triangles. It relates the ratios of the lengths of the sides to the sines of their opposite angles. The Law of Sines states:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those respective sides.

To find a missing angle of a non-right triangle using the Law of Sines, you will need to have at least two side lengths and one angle measure given or known. Let's consider the scenario where we are trying to find the measure of angle A.

1. Identify the given information: Look for the known side lengths and angle measures. For this case, let's assume we know the lengths of sides a and b.

2. Write down the Law of Sines equation: Using the given information, we can write the equation for the Law of Sines:

a/sin(A) = b/sin(B)

3. Substitute the known values: Plug in the values you know into the equation. In this case, substitute the lengths of sides a and b.

a/sin(A) = b/sin(B)

4. Rearrange the equation: Solve for the unknown angle by rearranging the equation to isolate the desired variable. In this case, we want to isolate angle A:

sin(A) = (a * sin(B)) / b

5. Use inverse trigonometric functions: Take the inverse sine (sin^(-1)) of both sides of the equation to solve for the unknown angle A:

A = sin^(-1)((a * sin(B)) / b)

6. Use a calculator or trigonometric tables: Substitute the known values for a, b, and B into the equation and evaluate the expression using a calculator or trigonometric tables to find the measure of the missing angle A.

Remember to use appropriate units and round your answer to the desired level of precision.

By following these steps and applying the Law of Sines, you can find the missing angle of a non-right triangle in pre-calculus.
These videos are designed to review and reteach Precalculus and Collegeboard Pre-CALC AP content. My videos cover functions, polynomials, exponential and logarithmic expressions, trigonometry, parametric equations, polar coordinates, vectors, matrices and systems, conic sections, discrete mathematics, sequences and series; and an introduction to calculus.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa .
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