1 / 11

Finding Areas with Trigonometry

Finding Areas with Trigonometry. Objectives. I can use trigonometry to find the area of a triangle. Practice. Find the area of a regular triangle with a side length of 18.6 meters. A B C D. A. 346 m 2 B. 299.6 m 2 C. 173 m 2 D. 149.8 m 2. Next Application….

yen-kelley
Download Presentation

Finding Areas with Trigonometry

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. Finding Areas with Trigonometry

  2. Objectives • I can use trigonometry to find the area of a triangle.

  3. Practice Find the area of a regular triangle with a side length of 18.6 meters. • A • B • C • D A. 346 m2 B. 299.6 m2 C. 173 m2 D. 149.8 m2

  4. Next Application… • Area of an oblique triangle • Given two sides of any triangle and the measure of an angle between them • Use trigonometry to find its surface area • Recall previous formula for the area of a triangle: A = ½ bh

  5. We will use an obtuse triangle • Label sides a, b, and c, opposite their corresponding angles • Draw a height, h, inside

  6. Next… • In order to use A = ½ bh, we need b and h, but all we know are a, b, and the measure of angle C (for example) we need “h”! • Look at triangle BDC inside: • How can we write a trig ratio using sides h and a? • We can use this to solve for “h”!

  7. So Far we have… • Solve this for “h”: h = a sin C • Now we have the info we need to use A = 1/2bh! • A = ½ bh substitute “a sin C” for “h” • A = ½ a b sin C

  8. IN CONCLUSION • The area of an oblique triangle is one-half the product of the lengths of two sides, times the sine of their included angle! • For any triangle, ABC Area = ½ bcsinA = ½ absinC = ½ ac sinB

  9. Practice • Find the area of a triangular lot having two sides of lengths 90m and 52m and an included angle of 102°. • Draw it: • Area = ½ (90)(52) sin 102 ≈ 2288.87 m2

  10. Practice • Find the area of a triangle with sides 6 and 10 and an included angle of 110° Round to the nearest hundredth. • Area = 28.19

  11. Practice • Find the area of a triangle with side lengths 92 and 30 with an included angle 130°. • Area = 1057.14

More Related