1 / 11

Right Triangle Trigonometry: Finding Trigonometric Ratios and Missing Parts

Learn how to use the lengths of the sides of a right triangle to find trigonometric ratios, solve applied problems, and determine missing parts of the triangle. Explore the concepts of sine, cosine, and tangent ratios with practical examples.

sness
Download Presentation

Right Triangle Trigonometry: Finding Trigonometric Ratios and Missing Parts

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHAPTER 10 Geometry

  2. 10.6 • Right Triangle Trigonometry

  3. Objectives Use the lengths of the sides of a right triangle to find trigonometric ratios. Use trigonometric ratios to find missing parts of right triangles. Use trigonometric ratios to solve applied problems.

  4. Ratios in Right Triangles • Trigonometry means measurement of triangles. • Trigonometric Ratios: Let A represent an acute angle of a right triangle, with right angle, C, shown here.

  5. Ratios in Right Triangles • For angle A, the trigonometric ratios are • defined as follows:

  6. Example: Becoming Familiar with The Trigonometric Ratios Find the sine, cosine, and tangent of A. Solution: Using the Pythagorean Theorem, find the measure of the hypotenuse c.

  7. Example: Finding a Missing Leg of a Right Triangle • Find a in the right triangle • Solution: Because we have a known angle, 40°, with a known tangent ratio, and an unknown opposite side, “a,” and a known adjacent side, 150 cm, we can use the tangent ratio. • tan 40° = • a = 150 tan 40° ≈ 126 cm

  8. Applications of the Trigonometric Ratios • Angle of elevation: Angle formed by a horizontal line and the line of sight to an object that is above the horizontal line. • Angle of depression: Angle formed by a horizontal line and the line of sight to an object that is below the horizontal line.

  9. Example: Problem Solving using an Angle of Elevation • Find the approximate height of this tower. • Solution: We have a right triangle with a known angle, 57.2°, an unknown opposite side, and a known adjacent side, 125 ft. • Using the tangent ratio: • tan 57.2° = • a = 125 tan 57.2° ≈ 194 feet

  10. Example: Determining the Angle of Elevation • A building that is 21 meters tall • casts a shadow 25 meters long. • Find the angle of elevation of the • sun. • Solution: We are asked to • find mA.

  11. Example continued • Use the inverse tangent key • The display should show approximately 40. Thus the angle of elevation of the sun is approximately 40°.

More Related