# Download Law of Cosines, Law of Sines, and Area (1)

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Myrecia Davis
Amaana Hinds
6th
Study Guide
Law of Sine
The Law of Sine provides a formula that relates the sides with the angles of a triangle. This
formula allows you to easily find the side length or the angle. The law of sin has angles and its
opposite sides. The law of sins can have two sides, one degree, and two degrees.
Formula
Examples
1.
Since this problem uses sides a and b, we need to know the sides of b.
Myrecia Davis
Amaana Hinds
2.
Since this problem uses side r and t, we need to know <S.
6th
Myrecia Davis
Amaana Hinds
Practice Problems:
For addition explaining, you can refer to the (pgs.582-585) in your textbook.
1.
2.
Video

https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/law-sinescosines/v/law-of-s
6th
Myrecia Davis
Amaana Hinds
Law of Sine Practice Problem Solutions
1.
2. First find m<A by using the Triangle Theorem.
Now, use the law of sine to help set up ratios.
6th
Myrecia Davis
Amaana Hinds
The Law of Cosine
Definition: The Square of a side of a plane triangle equals the sum of the squares of the remaining
sides minus twice the product of those sides and the cosine of the angle between them. The law of
cosines has two sides, or three sides.
Formula
Examples
1.
In, m<C = 42º, a = 19 and b = 26. Find the length of side c, to the nearest integer.
6th
Myrecia Davis
Amaana Hinds
6th
2.
This problem involves all three sides but only one angle of the triangle. This fits the profile for
the Law of cosines.
Myrecia Davis
Amaana Hinds
Practice Problems
If you need more explaining, you can refer to the (pgs.591-598).
.
2.
Video

https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/law-sinescosines/v/law-of-cosines-example
6th
Myrecia Davis
Amaana Hinds
Law of Cosine Practice Problem Solutions
1. Sin3522 = SinB38
Sin B = 38 x Sin3522 = 0.9907
2. Apply the law of cosines that involves θ.
=> b2 = a2 + c2 - 2ac cosθ
=> b2 = 102 + 52 - 2 * 10 * 5 cos45o
=> b2 = 100 + 25 - 100 *
= 125 - 70.9
= 54.1
=> b = 7.4 (approx)
12√
6th
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