Math 25 — Trigonometry
April 9, 2017
Name: Answer Key
David Arnold
Quiz #13 — Extra Credit
Instructions. (10 points) This quiz is open notes, open book. This includes any supplementary texts or
online documents. You are not allowed to work in groups or pairs on the quiz. You are not allowed to enlist
the aid of a tutor or friend to help with the quiz. You must answer all of the exercises on your own. You
are also not allowed to share your work with your fellow students.
Honor Pledge: I promise that the solution submitted was done entirely by me. I received no help from
colleagues, friends, or tutors. I also did not share any parts of my solution with any of my classmates.
Signature:
(10pts )
1. Consider the triangle 4ABC, where you are given the following information:
A = 50◦
a = 5 cm
b = 6 cm
Use a ruler, protractor, and compass to sketch all possible triangles with the given data. If there is more
than one possible triangle, put each triangle on a separate page along with the accompanying work for
that particular triangle. Once your triangle(s) are drawn, use your ruler and protractor to measure the
missing sides and angles. Next, use the law of sines to find all of the missing parts of each triangle you’ve
drawn, then find approximations of your exact solutions provided by the law of sines using Mathematica,
making sure they approximately agree with your measurements taken with your ruler and protractor. If
not, either draw a more accurate figure or check your law of sines work to look for a mistake. The point
here is to get your measurements made with ruler and protractor to closely agree with the measurements
predicted by the law of sines. To receive full credit, you must have two tables for A, B, C, a, b, and
c. The first must be your ruler and protractor measurements and the second must be your Mathematica
approximations of your exact solutions.
Solution: First Triangle: There are two different triangles you can draw with this information. Here
is the first.
C
6
5
50◦
A
c
We can now use the law of sines.
5
6
=
◦
sin 50
sin B
6 sin 50◦
sin B =
5
6 sin 50◦
−1
B = sin
5
B ≈ 66.8◦
B
Math 25 — Trigonometry/Quiz #13 — Extra Credit – Page 2 of 3 – Name: Answer Key
The sum of the angles of a triangle is 180◦ . Thus:
A + B + C = 180◦
50◦ + 66.8◦ + C = 180◦
C ≈ 63.2◦
Now we can use the law of sines again.
5
c
=
◦
sin 63.2
sin 50◦
5 sin 63.2◦
c=
sin 50◦
c ≈ 5.83
Hence:
• A = 50◦ , B = 66.8◦ , and C = 63.2◦ .
• a = 5, b = 6, and c = 5.83.
Second Triangle: Here is a picture.
C
6
A
50◦
c
5
B
We can now use the law of sines.
6
5
=
◦
sin 50
sin b
6 sin 50◦
sin B =
5
◦
−1
B = 180 − sin
6 sin 50◦
5
B ≈ 113.2◦
The sum of the angles of a triangle is 180◦ . Thus:
A + B + C = 180◦
50◦ + 113.2◦ + C = 180◦
C ≈ 16.8◦
Now we can use the law of sines again.
c
5
=
sin 16.8◦
sin 50◦
5 sin 16.8◦
c=
sin 50◦
c ≈ 1.89
Hence:
Math 25 — Trigonometry/Quiz #13 — Extra Credit – Page 3 of 3 – Name: Answer Key
• A = 50◦ , B = 113.2◦ , and C = 16.8◦ .
• a = 5, b = 6, and c = 1.89.