Download The Law of Cosines Investigation

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1. Can you use the Law of Sines to find all of the missing angles and sides of the following triangle? Why or why
not?
23 cm
28°
18 cm
Law of Cosines
When the Pythagorean Theorem or Law of Sines cannot be used to find a missing side
or angle then the Law of Cosines will work. This will occur when only two sides
and the included angle are given or when all sides but no angles are given.
Rule: a 2  b 2  c 2  2bcCosA
b 2  a 2  c 2  2abCosB
c 2  a 2  b 2  2abCosC
2. Use the Law of Cosines to solve for the missing side of the above triangle and then use the Law of Sines to find
the missing angles.
C
3. A surveryor at point A sights points B and C on either side of Wolverine
Pond. She finds the measure of the angle between the sightings to be 72°
B
and measures AB = 63 meters and AC = 78 meters.
a. Calculate, to the nearest tenth of a meter, the distance BC across the pond.
Show all your work.
b. Calculate the measure of the two remaining angles using the Law of Cosines.
A
4. Find the length of the missing side of the triangle using the Law of Cosines.
39
11 cm
15 cm
B
C
5. Find the length of all 3 missing angles of the triangle using the Law of Cosines.
A
55 cm
75 cm
B
6. A triangular park has sides 50m, 60m and 70m.
35 cm
C
a. Draw a picture of the park in the space given to the right.
b. Calculate the measure of all 3 angles in the park.
Show all your work.
Checkpoint:
Write a sentence for each question below:
a) When should Right Triangle Trigonometry be used to find missing parts of triangles?
b) When should the Law of Sines be used?
c) When should the Law of Cosines be used?