Similar Right Triangles-Introductions to Trigonometry

9th - 10th

In this geometry worksheet, students examine similar right triangles as the basis for the foundation of trigonometry. Students define the basic trigonometric functions and use a calculator to find the trigonometric value of an angle. The four page worksheet contains forty-six problems. Answers are not included.

Resource Details

Algebra I

Similar Parts Investigation

How tall is that flagpole? Your pupils might want to stand on each other's shoulders to answer this, but this activity is all about using the math knowledge they already possess. Using right triangle trigonometric ratios (SOH CAH TOA) and the Pythagorean theorem, young geometers solve real-world problems. 

Applying the Pythagorean Theorem in a Mathematical Context

Participants who use this resource will apply the Pythagorean Theorem to show whether or not the shaded triangle inscribed in a rectangle is a right triangle. Once all of the sides on the shaded triangle are found, it is important that your class understands that the largest side may be the hypotenuse. From there, it is easy to apply the Pythagorean Theorem to solution II of the commentary.

Ratios of Right Triangles

Students find the angle measures of a right triangle given two side lengths.  In this finding the angle measures of a right triangle given two side lengths lesson, students record the ratio of a leg and hypotenuse of a right triangle.  Students discuss why the ratio remains constant when a common vertice is manipulated.  Students find the angle measure of a right triangle using sine, cosine, and tangent ratios.

Investigating Trigonometric Ratios Through Similar Right Triangles

Students identify similar and congruent right triangles. In this geometry lesson, students use trigonometric ratios to identify missing sides and angles of a triangle. They differentiate similar and congruent triangles.

Investigating Trigonometric Ratios Through Similar Right Triangles.

49Students investigate the properties of right triangles. In this geometry lesson, students differentiate between similar and congruent triangles. They use the Pythagorean Theorem to find the missing angles and sides.

Trigonometric Functions of Acute Right Triangles

Students derive the six trigonometric functions. For this trigonometry lesson, students show their understanding of trigonometric functions as they relate the right triangles. They find the missing angles and side use trig ratios of sine, cosine and tangent.

Basic Trigonometry ll

Sal continues with examples of finding the sine, cosine, and tangent of an angle in a right triangle using SOH-CAH-TOA. In his examples, he reviews the use of the Pythagorean Theorem and rationalizing the denominator of a fraction. He also does an example of traditional 30-60-90 triangle and finds each of the three trigonometric ratios for the 30_ and 60_ angles. Note: After watching this video, there is a set of practice problems, titled �Trigonometry 1�, that would be worth trying.

Basic Trigonometry

This video introduces the basics of trigonometry. It starts by defining a right triangle and showing two different examples of finding the ratios of sine, cosine, and tangent using the SOH-CAH-TOA mnemonic. This resource could be used as a quick introduction or review.

Verifying Trig Ratios Using Similar Triangles

Students solve problems of a right triangle using properties of trigonometry. In this geometry lesson plan, students apply properties of a right triangle to solve problems correctly.

Solving Right Triangles Using Trigonometry

High schoolers examine and discuss techniques using trigonometric ratios for right triangles. They observe examples of trigonometric ratios, discuss alternative methods for checking their results, and complete a worksheet.

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