1. Solve the triangle given below C b Y 6 B 4 A • b = . Based on the length of the sides opposite them, which of the two unknown angles has a lesser measure? What is the degree measure of this angle? What is the degree measure of the remaining angle? 122° α
1. Solve the triangle given below C b Y 6 B 4 A • b = . Based on the length of the sides opposite them, which of the two unknown angles has a lesser measure? What is the degree measure of this angle? What is the degree measure of the remaining angle? 122° α
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
Sample solution included. Answer each questions.
![All values must be rounded off to 2 decimal places AND use these rounded off values when computing
for other missing values.
1. Solve the triangle given below
C
6
b
B
4
A
. b =
• Based on the length of the sides opposite them, which of the two unknown angles has a
lesser measure? What is the degree measure of this angle?
• What is the degree measure of the remaining angle?
Y
122°
α](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95aebdb0-ffda-4603-876a-48cfb74f753b%2F7d7e6543-f44a-4e56-b9ec-96784171c482%2Fkbs7opa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:All values must be rounded off to 2 decimal places AND use these rounded off values when computing
for other missing values.
1. Solve the triangle given below
C
6
b
B
4
A
. b =
• Based on the length of the sides opposite them, which of the two unknown angles has a
lesser measure? What is the degree measure of this angle?
• What is the degree measure of the remaining angle?
Y
122°
α
![Sample Problems (Time allotment: 20 minutes)
Let us apply the Law of Cosines in solving the problem in Situation 1.
Example 1 (SAS)
Find the value of b in the figure below.
B
12
A
α
b
Y
Solution. We are given a scenario wherein two sides and their included angle (SAS) are known. From
these, we are to determine the side opposite the included angle.
Using the Law of Cosines Eq. 2
b²=a²+c²-2ac cos B
Substituting the given values, we have
b²
10²+122-2(10)(12) cos 67°
b² 100+144-240 cos 67°
b=√100+144-240 cos 67° 12.3
Referring to the same problem, this time let us determine the remaining angle measures, namely, a and y.
We can use either Law of Sines or Law of Cosines to find these values.
Using the Law of Sines
sin 67°
sin a
10
12.3
10 sin 67°
sin α =
12.3
a=sin 10sin 67°
≈48.5°
12.3
And for the last angle, we can apply the Triangle Sum Theorem.
y=180° -67°-48.5° = 64.5°
Mathematics 4 Page 3 of 6
67°
10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95aebdb0-ffda-4603-876a-48cfb74f753b%2F7d7e6543-f44a-4e56-b9ec-96784171c482%2Fz25a9mn_processed.png&w=3840&q=75)
Transcribed Image Text:Sample Problems (Time allotment: 20 minutes)
Let us apply the Law of Cosines in solving the problem in Situation 1.
Example 1 (SAS)
Find the value of b in the figure below.
B
12
A
α
b
Y
Solution. We are given a scenario wherein two sides and their included angle (SAS) are known. From
these, we are to determine the side opposite the included angle.
Using the Law of Cosines Eq. 2
b²=a²+c²-2ac cos B
Substituting the given values, we have
b²
10²+122-2(10)(12) cos 67°
b² 100+144-240 cos 67°
b=√100+144-240 cos 67° 12.3
Referring to the same problem, this time let us determine the remaining angle measures, namely, a and y.
We can use either Law of Sines or Law of Cosines to find these values.
Using the Law of Sines
sin 67°
sin a
10
12.3
10 sin 67°
sin α =
12.3
a=sin 10sin 67°
≈48.5°
12.3
And for the last angle, we can apply the Triangle Sum Theorem.
y=180° -67°-48.5° = 64.5°
Mathematics 4 Page 3 of 6
67°
10
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