The Law of Sines for Finding Missing Side Lengths and Angle Measures
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We will learn to…
•
Apply
Law of Sines
to
find
missing
side lengths
and angle measures
of any triangle.
Law of Sines:
=
Law of Sines
is used to find missing _____________________ when you
are given _______________ and _________________. It can also be
used to find missing _____________________ when you are given
_______________ and _________________.
side lengths
=
c
b
=
=
two angles
one side
angle measures
two sides
one angle
Example 1:
Find the value of
A
. Round to nearest tenth
.
Given:
Finding:
Angle a = 45°
Side
A
Law of Sines?:
Yes!
Write Equation, Substitute, & Solve:
A
≈ 6.7 units
NOT Right Triangle!
Side B
= 6
39°
a
B
b
c
C
Angle b = 39°
=
=
=
=
6
=
9.534
*sin 45°
*sin 45°
A
=
9.534
*sin 45°
Example 2:
Find the value of
c
. Round to nearest tenth
.
Given:
Finding:
Angle c
Law of Sines?:
Yes!
Write Equation, Substitute, & Solve:
c
≈ 47°
NOT Right Triangle!
Side B
= 9
Angle b = 70°
=
=
=
c
=
46.959°
7
a
B
b
c
C
Side C
= 7
=
0.104
*7
7*
sin c
=
0.731
c
=
sin
-1
(0.731)
Example 3:
Find the area of the triangle. Round to tenth
.
Given:
Finding:
Area of Triangle
Law of Sines?:
Yes! (kinda sorta…)
Write Equation, Substitute, & Solve:
Area ≈ 19.7 units
2
NOT Right Triangle!
Side B
= 9
=
6
a
B
b
c
C
Side A
= 6
47°
Angle c = 47°
Area
=
Area
The Law of Sines is a fundamental concept in trigonometry that helps in finding missing side lengths and angle measures of any triangle. Through examples and explanations, this content teaches how to apply the Law of Sines to solve for unknowns in non-right triangles. It covers writing equations, substituting values, and solving for missing variables such as side lengths, angles, and the area of a triangle.
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Presentation Transcript
11/3: Apply the Law of Sines to find missing side lengths and angle measures for any triangle. Do Now Agenda Homework DO NOW! & Check On your desk: Handout - Pencil & Calculator (8 problems) -Today s Handouts Guided Notes Independent Practice Unit 1 Test MONDAY 11/14! DO NOW! Homework! (maybe ) Start studying now!
We will learn to Apply Law of Sines to find missing side lengths and angle measures of any triangle.
Law of Sines: sin c sin b sin a = = b C C B A A a c A C B B = = sin c sin a sin b side lengths one side one angle Law of Sines is used to find missing _____________________ when you are given _______________ and _________________. It can also be used to find missing _____________________ when you are given _______________ and _________________. two angles angle measures two sides
Example 1:Find the value of A. Round to nearest tenth. Given: NOT Right Triangle! Write Equation, Substitute, & Solve: b sin c sin a sin b = 39 = C Angle a = 45 Angle b = 39 C A B A 45 Side B= 6 a sin 39 6 6 sin 45 A A = c 6 B Finding: Side A = sin 45 sin 39 A Law of Sines?: Yes! = *sin 45 9.534 *sin 45 sin 45 A= 9.534*sin 45 A 6.7 units
Example 2:Find the value of c. Round to nearest tenth. Given: NOT Right Triangle! Angle b = 70 Write Equation, Substitute, & Solve: b sin c sin a sin b C = = 70 7 C A B A Side B= 9 Side C= 7 a sin c 7 sin 70 9 = c 9 B Finding: Angle c sin c 7 sin c 7* 0.104 *7 = Law of Sines?: Yes! 0.731 = sin-1(0.731) = c c = 46.959 c 47
Example 3:Find the area of the triangle. Round to tenth. Given: NOT Right Triangle! Angle c = 47 Write Equation, Substitute, & Solve: b C sin * side 2 * side 1 Area = A 6 2 Side A= 6 Side B= 9 47 a *9* 6 sin 47 Area c = 9 B 2 Finding: Area of Triangle Area 19.7 units2 Law of Sines?: Yes! (kinda sorta )
