Trigonometric Ratios Teacher Resources

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Young scholars explore the concept of trigonometric ratios.  In this trigonometric ratios lesson, students use trigonometric ratios and the angle of elevation/depression to determine the height of an object.  Young scholars use their clinometer made from a protractor, string, hex nut, and tape to determine the angle of depression/elevation of an object or building.  Students determine the height of the object or building using trigonometric ratios.
Astrolabes have been used by explorers and astronomers throughout the ages. But how exactly do they work and what can a young mathematician do with one today? High schoolers will build a simple version of this tool and then using the altitude, measure the height of various objects. Accompanying worksheets guide learners through different discoveries using their knowledge of similar triangles and trigonometric ratios. 
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. 
Maybe your class wouldn't be taking a field trip to a rocket launching site, but the ideas presented here could be used for a new by clock tower, tree, or telephone pole. Learners use trigonometric ratios to determine the heights of tall structures. They convert their calculations for standard to metric units using an Internet site.
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.
What's a trigonometric ratio? It 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 divided by the hypotenuse to find sin(A). The instructor draws a diagram and labels all the sides and angles. She then explains how to apply the formula to find sin(A).
Eighth graders use trigonometric ratios for finding a missing angle or side of a right triangle. Use of TI-83 calculator is utilized within this lesson plan. Students identify and use the trigonometric ratios to solve problems with right triangles.
In this finding trigonometric ratios worksheet, 11th graders solve and complete 22 various types of problems. First, they find the value of each trigonometric ratio to the nearest ten-thousandth. Then, students use a calculator to find the value of each ratio.
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.
In this trigonometric ratios worksheet, students use trigonometric ratios to complete indirect measurement word problems.  This three-page worksheet contains 3 problems.

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Your collaborative geometry learners use trigonometric ratios and a clinometer that they assemble themselves to indirectly measure the height of a flag pole and other objects. Then they create a presentation to explain the process they used and present it to their classmates in a gallery walk.
The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle to solve. Here the objective is to get geometry learners develop an understanding of two new solutions. One using congruent triangles, and the other using trigonometric ratios. 
What's a trigonometric ratio? It is a ratio between two sides of a right triangle. In this problem, find cosine(A) in the given right triangle. Use the ratio of the adjacent side divided by the hypotenuse to find cos(A). The instructor draws a diagram and labels all the sides and angles. She then explains how to apply the formula to find cos(A).
What's a trigonometric ratio? It is a ratio between two sides of a right triangle. In this problem, find tangent(A) in the given right triangle. Use the ratio of the opposite side divided by the adjacent side to find tan(A). The instructor draws a diagram and labels all the sides and angles. She then explains how to apply the formula to find tan(A).
Use this complete lesson plan to introduce geometers to inverse trigonometric functions. Learners use trigonometric ratios to solve triangles when an angle measure is known, then explore using the inverse process when only side lengths are given. The exploration naturally leads to a discussion about use of the inverse trigonometric function keys on the calculator. The lesson also includes five practice problems, three of which are real-world scenarios. Each practice problem has multiple parts.
Learners calculate the sides of right triangles in this trigonometric ratios lesson. They use Cabri Jr. software and TI-83 or TI-84 calculators to find the side lengths and their ratios to each other for various triangles. The provided chart helps your learners see patterns in the ratios.
In this trigonometric ratios worksheet, students solve and complete 10 various types of problems. First, they write the degrees listed in radian measure. Then, students find the exact ratios for each equation. They also find the value of x in each triangle and evaluate.
Students study the concept of tangent of a unit circle. In this unit circle lesson, students explore the mathematical history of the trigonometric ration, tangent, through an interactive date-gathering construction that simulates an experience that mirrors how values of trig functions may have been approximated.
The class uses the computers to access GeoGebra Dynamic Worksheets to learn the basics about vectors. They will look at graphs and make computations to problem solve to find coordinates of vectors.  
In this trigonometry ratios in right triangles worksheet, 10th graders solve 10 different trigonometric ratios that apply to right triangles. First, they define a trigonometric ratio and its three most common ratios, sine, cosine, and tangent. Then, students find the indicated trigonometric ratio as a fraction and as a decimal rounded to the nearest ten-thousandth.

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