IXL - Law of Cosines (Geometry practice)

Find

19°

Write your answer as an integer or as a decimal rounded to the nearest tenth.

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Learn with an example

question

Find

28°

Write your answer as an integer or as a decimal rounded to the nearest tenth.

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

solution

Since you know the lengths of two sides and the measure of the included angle

(

and

∠

use the Law of Cosines to find

the length of the remaining side.

–

cos

(

)

–

cos

28°

289

225

–

510

cos

28°

289

225

–

510

0.882…

63.696…

7.981…

To the nearest tenth,

≈

8.0

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Not feeling ready yet? These can help:

Q.10Inverses of trigonometric functions

Q.8Find trigonometric functions using a calculator

B.2Evaluate variable expressions involving integers

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