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Geometry/Trig
Lesson 13-9: Final Exam Review 9
[Unit 11: Non-Right Triangle Trigonometry]
Name: ______________________________
Date: _______________________________
Learning Goals Achieved in this Unit
1. How do we use the Law of Sines to solve for missing sides/angles in a non-right triangle?
2. How do we use the Law of Cosines to solve for missing sides/angles in a non-right triangle?
3. How can I apply Law of Sines and Law of Cosines to real-world applications of non-right triangle trigonometry?
When to use each Law:
 When given two sides and two angles use
the _______________________________, including
what we are finding!

When given three sides and one angle
use the ________________________________
including what we are finding!
Law of Cosines (to find a side):
2
2
Law of Sines:
𝑎
=
𝑆𝑖𝑛(𝐴)
Law of Cosines (to find an angle):
The angle we are looking for must always
correspond with a
2
The side you are looking for must always
be __________________________ with the angle
used

a is always the side we are looking for
Don’t forget to ___________________________ your
final answer
𝐶𝑜𝑠(𝐴) =




𝑆𝑖𝑛(𝐵)
*Corresponding means __________________________ or
across from*
𝑎 = 𝑏 + 𝑐 − 2𝑏𝑐 ∙ 𝐶𝑜𝑠(𝐴)

𝑏
(𝑏 2 +𝑐 2 −𝑎2 )
(2𝑏𝑐)
A is always the angle we are looking for
DO NOT forget to USE PARANTHESIS around the
numerator AND denominator
Inverse Cosine your answer to find an _____________
Other Things to Remember:
When finding an angle you must use ___________________________________________

Lower case letters represent ___________________ of a triangle. The sides and are always opposite
their corresponding angle.

Included angle: Angle in between the two given sides.

First always determine which law to use before setting up your equation!

Sometimes you need to find an angle before you begin using one of the laws

Don’t forget to round and label your units!
Geometry/Trig
Let’s Analyze a Student Sample and Correct the Work!
As you look over this sample, make corrections in a different color!
STUDENT SAMPLE
Notes
A playground is being built in the shape of the
triangle ABC below. Find the length of the
missing side AB of the playground rounded to
the nearest hundredth.
What did the
student do well?
Our Corrections
What mistake(s) did
the student make?
Let’s Try One Together!
A cross country race is taking place, and Matt is trying to
figure out the distance of the course. He receives a map of
the course, which is in the shape of a triangle. However, the
map he receives was misprinted. He only has 5 minutes
until the race starts, and he wants to know how far he will
have to run in order to complete the course.
a. Find the missing side of the triangular trail that was misprinted to the nearest meter.
Geometry/Trig
b. Calculate the total distance Matt with run during his race.
Your Turn!
1. In triangle DEF, d = 65, f = 40, and m∠𝐸 = 22°. Which equation can be used to determine the value of e?
(Hint: Draw a picture first)
a. 652 = 402 + 𝑒 2 − 2(65)(𝑐)cos(22°)
b. 𝑒 2 = 402 + 652 − 2(40)(65)cos(22°)
c. 𝐶𝑜𝑠(22°) =
402 +652 −𝑒 2
(40)(65)
d. 402 = 652 + 𝑒 2 − 2(40)(𝑐)cos(22°)
2. Given the following triangle, what property/law would I use to solve for the missing side x?
a. Law of Cosines
b. SOH CAH TOA
c. Law of Sines
d. Pythagorean Theorem
3. In the accompanying diagram of Δ𝐴𝐵𝐶, 𝑚∠𝐴 = 80°, 𝑚∠𝐵 = 43° and side BC = 25.
What is the length of side AB to the nearest tenth?
a.
b.
c.
10.1
36.1
17.3
Geometry/Trig
d. 18.5
4. Find the smallest angle to the nearest tenth of a degree of a triangle whose sides are 8, 12,19.
a. Which law will we use here?
b. Find the measurement of the smallest angle to the nearest tenth of a degree.
5. A playground is being built in the shape of the triangle ABC below. Using either law, find the length of the
missing side BC of the playground rounded to the nearest whole number.
Geometry/Trig
6. The diagram below shows displays triangle ABC.
a) Find the missing side to the nearest tenth.
b) Find the perimeter of triangle ABC.
7.
a. What is the measure of∡𝑁?
b. Find the missing side of the following triangle. Round your answer to
the nearest hundredth.
Geometry/Trig
8. Given triangle QRS, m∡𝑆 = 71°, 𝑠𝑖𝑑𝑒 𝑄𝑆 = 400𝑓𝑡, 𝑎𝑛𝑑 𝑠𝑖𝑑𝑒 𝑄𝑅 = 570𝑓𝑡. Find the measurement of ∡𝑅 to the
nearest degree.