Unit 8 Exam Review
Pre-Calculus Honors Unit 8 Review Answer Key
1. List the given cases where the Law of Sine’s is the most appropriate method to use to
solve for a triangle and when the Law of Cosine’s is the most appropriate method to use
to solve for a triangle.
Law of Sines
Law of Cosines
ASA
SSS
AAS
SAS
SSA (Ambiguous Case)
2. Which case do you have to check if 0, 1, or 2 triangles can be formed? SSA
In your own words, explain how you decided if 1 triangle is formed or if 2 triangles may be
formed using the given information? When you take the inverse of sine you are given the angle
in quadrant 1 and must find the supplementary pair angle. If the sum of the given angle and the
supplementary pair angle is greater than 180 degrees you have 1 triangle. If the sum is less than
180 degrees you have 2 triangles. If you get error when taking the sine inverse you have 0
triangles.
In 3-6, find the remaining angle(s) and side(s) of each triangle, if it exists. If no triangle exists,
say “No triangle”. Round answers to one decimal place.
3.)
4.)
c = 15.6cm
b = 9cm
< A = 130.8°
< B = 14.6°
< C = 95°
< C = 34.6°
5.)
6.)
< B = 64.2° < B = 115.8°
< C = 95.4° < C = 43.8°
c = 34.3cm c = 23.8cm
< B = 135.4°
< C = 17.6°
b = 27.8cm
Unit 8 Exam Review
7. A pilot has just started on the glide path for landing at an airport with a runway length of 1.7
miles. The angles of depression from the plane to the ends of the runway are 19.4 degrees and
20.7 degrees
(a) Draw a diagram that visually represents the problem
(b) Find the air distance the plane must travel until touching down on the near end of
the runway. 24.9 miles
(c) Find the ground distance the plane must travel until touching down on the near
end of the runway. 23.3 miles
(d) Find the altitude of the plane when the pilot begins descending.
8.8 miles
Challenge #1: In the figure below, a beam of light is directed at the blue mirror, reflected to the
red mirror, and then reflected back to the blue mirror. Find the distance PT, which the light
travels from the red mirror to the blue mirror.
Step 1 Find PQ = 2.64
Step 2 Find
a = 48.8°
Step 3 Find < OPQ = 106.2 degrees
Step 4 Find
q =180 -106.2 = 73.8°
Step 5 Find <TPQ = 106.2-73.8 = 32.4 degrees
Step 6 Find PT using the Law of Sines = 2.01 feet
c
62
2
Unit 8 Exam
1 Review
49°
C
B
80
Challenge #2: Find the missing lengths and angle measurements in the figure below. Round all
answers to the nearest tenth.
2)
A
76°
63
m
E 4
3 53°
r
D
5
n
p
50
p = 51
n = 111.2
< 2 = 98°
r = 36.2
< 3 = 67.5°
< 5 = 70.5°
< 1 = 33.3°
< 4 = 70.7°
m = 10.9
42°
27°
2
C
92
1
B