EQ: What is the law of sines, and how can we use it to solve right triangles?
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EQ: What is the law of sines, and how can we use it to solve right triangles?
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EQ: What is the law of sines, and how can we use it to solve right triangles?. EQ: What is the law of sines, and how can we use it to solve right triangles?. The Law of Sines allows you to solve a triangle as long as you know either of the following:. - PowerPoint PPT Presentation
Transcript of EQ: What is the law of sines, and how can we use it to solve right triangles?
EQ: What is the law of sines, and how can we use it to solve right triangles?
The Law of Sines allows you to solve a triangle as long as you know either of the following:
1. Two angle measures and any side length–angle-angle-side (AAS) or angle-side-angle (ASA) information
2. Two side lengths and the measure of an angle that is not between them–side-side-angle (SSA) information
EQ: What is the law of sines, and how can we use it to solve right triangles?
Using the Law of Sines for AAS and ASA
Solve the triangle. Round to the nearest tenth.
Step 1. Find the third angle measure.
mD + mE + mF = 180°
33° + mE + 28° = 180°
mE = 119°
Triangle Sum Theorem.
Substitute 33° for mD and 28° for mF.
Solve for mE.
EQ: What is the law of sines, and how can we use it to solve right triangles?
Step 2 Find the unknown side lengths.
sin D sin Fd f
=sin E sin F
e f=
sin 33° sin 28°d 15=
sin 119° sin 28°e 15=
d sin 28° = 15 sin 33° e sin 28° = 15 sin 119°
d = 15 sin 33°sin 28°
d ≈ 17.4
e = 15 sin 119°sin 28°
e ≈ 27.9Solve for the
unknown side.
Law of Sines.
Substitute.
Crossmultiply.
EQ: What is the law of sines, and how can we use it to solve right triangles?
Using the Law of Sines for AAS and ASA
Solve the triangle. Round to the nearest tenth.
Step 1 Find the third angle measure.
mP = 180° – 36° – 39° = 105° Triangle Sum Theorem
Q
r
EQ: What is the law of sines, and how can we use it to solve right triangles?
Solve the triangle. Round to the nearest tenth.
Step 2 Find the unknown side lengths.
sin P sin Qp q= sin P sin R
p r=Law of Sines.
sin 105° sin 36°10 q= sin 105° sin 39°
10 r=Substitute.
q = 10 sin 36°sin 105°
≈ 6.1 r = 10 sin 39°sin 105°
≈ 6.5
Q
r
EQ: What is the law of sines, and how can we use it to solve right triangles?
Solve the triangle. Round to the nearest tenth.
Step 1 Find the third angle measure.
mK = 31° Solve for mK.
mH + mJ + mK = 180°
42° + 107° + mK = 180°Substitute 42° for mH
and 107° for mJ.
EQ: What is the law of sines, and how can we use it to solve right triangles?
Step 2 Find the unknown side lengths.
sin H sin Jh j
=sin K sin H
k h=
sin 42° sin 107°h 12=
sin 31° sin 42°k 8.4=
h sin 107° = 12 sin 42° 8.4 sin 31° = k sin 42°
h = 12 sin 42°sin 107°
h ≈ 8.4
k = 8.4 sin 31°sin 42°
k ≈ 6.5Solve for the
unknown side.
Law of Sines.
Substitute.
Crossmultiply.
EQ: What is the law of sines, and how can we use it to solve right triangles?
Solve the triangle. Round to the nearest tenth.
Step 1 Find the third angle measure.
mN = 180° – 56° – 106° = 18° Triangle Sum Theorem
EQ: What is the law of sines, and how can we use it to solve right triangles?
Solve the triangle. Round to the nearest tenth.
Step 2 Find the unknown side lengths.
sin N sin Mn m= sin M sin P
m p=Law of Sines.
Substitute.sin 18° sin 106°1.5 m=
m = 1.5 sin 106°sin 18°
≈ 4.7 p = 4.7 sin 56°sin 106°
≈ 4.0
sin 106° sin 56°4.7 p=
EQ: What is the law of sines, and how can we use it to solve right triangles?
