Similar Right Triangles-Introductions to Trigonometry

9th - 10th

For 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

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.

Solve Right Triangle

In this trigonometric applications worksheet, students solve for the missing side of a right triangle using a trigonometric ratio. There are 46 questions, 10 of which are word problems.

Investigating Trigonometric Ratios Through Similar Right Triangles.

49Students investigate the properties of right triangles. In this geometry instructional activity, 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. In 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.

Ratios of Right Triangles

Tenth graders explore right triangle trigonometry.  For this geometry lesson, 10th graders investigate the sine and cosine ratios for right triangles.  The use of Cabri Jr. allows for measurement of side lengths and angles and allows students to examine of the ratios and to form and verify conjectures.

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.

Geometric Mean and Congruent Right Triangle

Students investigate right triangles using the six trigonometric identities. In this geometry lesson, students examine why the altitude in a right triangle creates two or more right triangles.

How Do You Find a Missing Side of a Right Triangle Using Cosine?

Trigonometry? What's trigonometry. Well, something to do with triangles, right? Right! Right triangles! In this problem, find the missing length of one of the sides. So set this up as a ratio: cosine(A) = adjacent side length divided by the length of the hypotenuse. Still not sure what to do? Then watch this video as the instructor walks through the steps.

Solving Right Triangles Using Trigonometry

Students 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.

How Do You Find the Sine of an Angle in a Right Triangle?

A trigonometric ratio is a ratio between two sides of a right triangle. In this problem, find sin(A) in the given right triangle. Use the ratio of the opposite side over the hypotenuse.

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