Finding Areas with Trigonometry

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# Finding Areas with Trigonometry - PowerPoint PPT Presentation

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
• 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 m2

B. 299.6 m2

C. 173 m2

D. 149.8 m2

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
• Label sides a, b, and c, opposite their corresponding angles
• Draw a height, h, inside
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…
• 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
• 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

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

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