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Published byJeffry Golden Modified over 8 years ago

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**Honors Geometry Sections 10.1 & 10.2 Trigonometric ratios**

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The word “trigonometry” comes from two Greek words which mean ___________________ And that is exactly what we will do with trigonometry - we will find the measures of angles and the length of sides in triangles. Initially, we will consider only right triangles, but later in this section, we will consider trigonometry involving acute and obtuse triangles. triangle measurement

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**A trigonometric ratio (i. e**

A trigonometric ratio (i.e. fraction) is a ratio of the lengths of two sides of a right triangle. The three basic trigonometric ratios are sine (___), cosine (___) and tangent (___). These ratios are defined for the acute angles of a right triangle as follows.

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**sin A = -------------- cos A = -------------- tan A = -------------**

opposite leg hypotenuse adjacent leg hypotenuse If we write the ratios for the acute angle B instead, then the opposite leg and adjacent leg would be switched!!!! opposite leg adjacent leg

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**An easy way to remember these three trig ratios is with the mnemonic**

SOH-CAH-TOA I N E P Y P O S D J Y P AN P D J

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**Example: Give the three trig ratios for the following triangles.**

3 5 4 5 3 4

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**Example: Give the three trig ratios for the following triangles**

Example: Give the three trig ratios for the following triangles. Sin O = Cos G = Tan G =

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The value of the sine, cosine and tangent of an angle depend only upon the measure of the angle and not the size of the triangle that the angle is found in. Here’s why!!! Therefore,

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Therefore, Now, we can take the first two ratios separately and rearrange the terms to get Note: These are the ratios for sin C in both Similarly, we can take the first and third ratios separately and rearrange the terms to get Note: These are the ratios for cos C in both

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A scientific calculator can be used to find the value of these three trig ratios. Make sure your calculator is in degree mode. sin 130 = ___________ cos 770 = ____________ tan 400 = ____________

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**We can use the trig ratios to find the lengths of unknown sides in right triangles.**

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**Example: Solve for x and y. Round your answers to the nearest 1000th.**

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**Example: Solve for x and y. Round your answers to the nearest 1000th.**

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Example: The angle of elevation to the top of a tree from a point 100 feet from the base of the tree is Estimate the height of the tree to the nearest 1000th. NOTE: the angle of elevation is the angle formed by a horizontal line (usually the ground) and the line of sight up to some object.

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Example: The angle of elevation to the top of a tree from a point 100 feet from the base of the tree is Estimate the height of the tree to the nearest 1000th.

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