5.3 Right Triangle Trigonometry
G.2.3 Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent;
Chart of Side Ratios to Reference Angles
As I understand it a long long time ago, mathematicians were studying triangles. They, like us, already understood how the properties of two similar triangles helped find missing sides and angles (just like in our opener activity). However, in every real world scenario, there are not always two similar triangles readily available.
Therefore some mathematician from India or Egypt (...its debatable...so we will say somewhere in the Middle East) started analyzing the measurements of different right triangles to create a resource for his fellow mathematicians, scientists, engineers, and sailors as reference.
Let’s see a re-enactment ...
As I understand it a long long time ago, mathematicians were studying triangles. They, like us, already understood how the properties of two similar triangles helped find missing sides and angles (just like in our opener activity). However, in every real world scenario, there are not always two similar triangles readily available.
Therefore some mathematician from India or Egypt (...its debatable...so we will say somewhere in the Middle East) started analyzing the measurements of different right triangles to create a resource for his fellow mathematicians, scientists, engineers, and sailors as reference.
Let’s see a re-enactment ...
Using the table to the right, answer the following questions:
- Approximate the adj/hyp side ratio (or Cos A) for a 40 degree reference angle. Answer
- Approximate the measure of the acute angle A in a right triangle to the nearest degree given that the opp/adj side ratio (or Tan A) is 1.93 Answer
- Approximate the measure of the acute angle A in a right triangle to the nearest degree given that the opp/hyp side ratio (or Sin A) is 0.34 Answer
Page 3 of Lesson