Warm – up Given the following triangle find the missing side lengths. 1. 2.

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Presentation transcript:

Warm – up Given the following triangle find the missing side lengths

Trigonometric Ratios Section

Standards MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles. Discover the relationship of the trigonometric ratios for similar triangles.

Essential Question How do I find the sine, the cosine, and the tangent of an acute angle?

Vocabulary Trigonometric ratio – a ratio of the lengths of two sides of a right triangle. Three basic trigonometric ratios: Sine (abbreviation: sin) Cosine (abbreviation: cos) Tangent (abbreviation: tan)

Trigonometric Ratios Let ∆ABC be a right triangle. The sine, the cosine, and the tangent of the acute angle  A are defined as follows:

S O H C A H T O A sin = opp/hyp cos = adj/hyp tan = opp/adj

Example 1 Find the sine, the cosine, and the tangent of the indicated angle. Round to 4 decimal places! a.  S b.  R

Try This! Find the sine, the cosine, and the tangent of the indicated angle. Round to 4 decimal places! a.  D b.  E

Example 2 Find the value of the variable. Round to the nearest tenth.

Try This! Find the value of the variable. Round to the nearest tenth.

Example 3 Find the value of the variable. Round to the nearest tenth.

Try This! Find the value of the variable. Round to the nearest tenth.

Vocabulary Angle of Elevation – When you stand and look up at a point in the distance, the angle that your line of sight makes with a line drawn horizontally. Angle of Depression – When you stand at an elevated point and look down at a point in the distance, the angle that your line of sight makes with a line drawn horizontally.

Example 4 You are measuring the height of a tree. You stand 45 feet from the base of the tree. You measure the angle of elevation to the top of the tree to be 59 . Find the height of the tree to the nearest tenth of a foot.

Summarizer

Classwork Worksheet

Homework Pages 159 – 160 Number 2 – 20 even Page 166 – 167 Number 2 – 20 even, 26