Why Isn't the Law of Tangents Taught in High School Trigonometry?

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In summary, the law of tangents is a trigonometric law that can be used to find missing sides or angles in a triangle. It is not commonly taught in public high school trigonometry courses in the USA, possibly because it is equivalent to the more commonly taught law of sines.
  • #1
mathdad
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When students are first taught trigonometry in public high schools across the USA, they eventually learn about the law of sines and law of cosines. However, the law of tangents is not taught.

1. What is the law of tangents?

2. What is the usefulness of this law?

3. Why do YOU think the law of tangents in not taught in most trig courses?
 
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  • #2
RTCNTC said:
When students are first taught trigonometry in public high schools across the USA, they eventually learn about the law of sines and law of cosines. However, the law of tangents is not taught.

1. What is the law of tangents?

I have heard of it, but never learned it or used it. I had to look it up:

Law of tangents

RTCNTC said:
2. What is the usefulness of this law?

It can be used in any case where two sides and the included angle, or two angles and a side, are known.

RTCNTC said:
3. Why do YOU think the law of tangents in not taught in most trig courses?

Perhaps because it is equivalent to the law of sines, which is simpler to recall? :D
 
  • #3
MarkFL said:
I have heard of it, but never learned it or used it. I had to look it up:

Law of tangents
It can be used in any case where two sides and the included angle, or two angles and a side, are known.
Perhaps because it is equivalent to the law of sines, which is simpler to recall? :D

I asked three questions in the other post about the car distance. I look forward to your answers.
 

FAQ: Why Isn't the Law of Tangents Taught in High School Trigonometry?

What is the Law of Tangents?

The Law of Tangents is a mathematical rule that relates the angles and sides of a triangle. It states that the ratio of the difference of the tangents of two angles in a triangle is equal to the ratio of the difference of the opposite sides of those angles.

How is the Law of Tangents different from the Law of Sines and Law of Cosines?

The Law of Tangents is specifically used for right triangles, while the Law of Sines and Law of Cosines can be used for any triangle. Additionally, the Law of Tangents only involves tangent functions, while the other laws involve sine and cosine functions.

When is the Law of Tangents used?

The Law of Tangents is often used in trigonometry and geometry to solve for missing angles or sides in a right triangle. It can also be used to determine the distance between two objects using angles and known distances.

How is the Law of Tangents derived?

The Law of Tangents can be derived from the Pythagorean theorem and the definition of tangent as the ratio of opposite and adjacent sides of a right triangle. It can also be derived from the Law of Cosines.

Are there any limitations to the Law of Tangents?

The Law of Tangents can only be used for right triangles and is not applicable for other types of triangles. It also assumes that the angles and sides of the triangle are known, and cannot be used to find unknown angles or sides without additional information.

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