Trigonometric Ratios in Right Triangles. Trigonometric Ratios are based on the Concept of Similar Triangles!

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Presentation transcript:

Trigonometric Ratios in Right Triangles

Trigonometric Ratios are based on the Concept of Similar Triangles!

All 45º- 45º- 90º Triangles are Similar! 45 º

All 30º- 60º- 90º Triangles are Similar! 1 60º 30º ½ 60º 30º º 30º 1

All 30º- 60º- 90º Triangles are Similar! 10 60º 30º º 30º º 30º

Naming Sides of Right Triangles   

We will be learning 3 trig ratios Sine- Abbreviation is Sin (but you pronounce it Sign, not Sin!!!) Cosine- Abbreviation is Cos Tangent- Abbreviation is Tan

 The Trigonometric Ratios (The SOHCAHTOA model)

A little trick to help you remember… Some Old Horse, Caught Another Horse, Taking Oats Away

Find the value of each of the trigonometric functions of the angle Adjacent c = Hypotenuse = 13 b = Opposite = 12

In order to use your calculator to find trigonometric ratios, it MUST be in degree mode!!!! Hint: Before taking ANY test that might have trig on it, change the mode to Degree to be safe (EOC, ACT, Semester Exam…)

Use a calculator to find each value. Round to the nearest ten thousandth.

Solving a Problem with the Tangent Ratio 60º 53 ft h = ? We know the angle and the side adjacent to 60º. We want to know the opposite side. Use the tangent ratio: 1 2 Why?