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Finding Areas with Trigonometry PowerPoint Presentation

Finding Areas with Trigonometry

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Finding Areas with Trigonometry

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Finding Areas with Trigonometry

- I can use trigonometry to find the area of a triangle.

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

- 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

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

- 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”!

- How can we write a trig ratio

- 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

- 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

- 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

- 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

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