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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….

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Presentation Transcript
objectives
Objectives
  • I can use trigonometry to find the area of a triangle.
practice
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

next application
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
we will use an obtuse triangle
We will use an obtuse triangle
  • Label sides a, b, and c, opposite their corresponding angles
  • Draw a height, h, inside
slide6
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”!

so far we have
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
in conclusion
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

practice1
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

practice2
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
practice3
Practice
  • Find the area of a triangle with side lengths 92 and 30 with an included angle 130°.
  • Area = 1057.14
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