IXL - Solve a triangle (Algebra 2 practice)

In solving this triangle, which law must you use first?

25°

Law of Sines

Law of Cosines

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question

In solving this triangle, which law must you use first?

86°

27°

Law of Sines

Law of Cosines

key idea

The Law of Cosines states

a
2
=
b
2
+
c
2
–
2
b
c
cos
(
A
)
b
2
=
a
2
+
c
2
–
2
a
c
cos
(
B
)
c
2
=
a
2
+
b
2
–
2
a
b
cos
(
C
)

where each lowercase letter (like

)

is the length of the side opposite the vertex labeled with the same capital letter (like

If you know the lengths of two sides and the measure of the included angle (like

and

∠

you can use the Law of Cosines to solve for the length of the third side (like

If you know the lengths of all three sides (like

and

First, use the Law of Cosines to solve for the cosine of an angle (like cos
A
,
cos
B
,
or cos
C
)
Then, use the inverse cosine function
(
cos
–
1
)
to solve for the measure of that angle. This works because
cos
-1
[
cos
(
x
)
]
=
x
if
0°
≤
x
≤
180°
,
and the measure of any angle in a triangle is in that range.

The Law of Sines states

sin

(

)

sin

(

)

sin

(

)

If you know the measures of two angles and the length of one's opposite side (like

∠

and

you can use the Law of Sines to solve for the length of the other angle's opposite side (like

solution

Since you know the measure of

∠

the length

of its opposite side, and the measure of

∠

you can use the Law of Sines to find the length

of the side opposite

∠

sin

(

)

sin

(

)

Since you only know one side length, you can't start with the Law of Cosines.

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Not feeling ready yet? These can help:

JJ.1Law of Sines

JJ.2Law of Cosines

II.18Solve a right triangle

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