IXL - Solve a triangle (Geometry practice)

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

109°

27°

Law of Sines

Law of Cosines

ref_doc_title.

Learn with an example

question

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

12°

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 lengths of two sides and the measure of the included angle

(

and

∠

you can use the Law of Cosines to find

the length of the remaining side.

–

cos

(

)

Since the only angle whose measure you know is

∠

and you don't know the length

of its opposite side, you can't start with the Law of Sines.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

R.1Law of Sines

R.2Law of Cosines

Q.13Solve a right triangle

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