Geometry
Name_____________ _______
Review - I fought the Laws (of Sine and Cosine) and…
The Laws Won!
Law of Sine
Law of Cosine
To solve each problem below, draw an appropriate picture and show your work!
1. Two ships leave the harbor at Boston. The angle between their paths is 43 degrees. One ship is
traveling at a rate of 35 miles an hour; the other ship is traveling at a rate of 25 miles per hour. At
the end of two hours, what is the distance between the two ships?
2. A Delta Airlines flight from Houston to Cincinnati, a distance of 1029 miles, encounters a violent
thunderstorm immediately after takeoff and flies off course by 22.5° for 400 miles, how far is the
plane from Cincinnati?
3. In the triangle below, find the measure of angle B, the length of AB, and the length of AC.
B
18
A
40°
55° C
4. There are three boats off the coast of Long Beach, CA. The captain of boat M knows that boat N
is 4.5 miles away and boat P is 5.3 miles away. He measures the angle between the two sightings
to be 40 degrees.
a. How far apart are boats N and P?
b. What is the angle between boats M and P, from the perspective of boat N?
5. Melissa and Rosa are golfing on a beautiful summer day. T he ninth hole is 380 yards. Melissa
hooked her drive on hole #9, as shown below. How far is Melissa’s ball from the hole?
380 yd
Tee
16°
310 yd
Ball
6. A triangular region has sides measuring 25, 35, and 15 feet. Find the measure of the angles in the
region.
7. To know how much paint is needed for a barn, a farmer is estimating the total surface area of the
barn. One part of the surface is triangular, as sketched below.
a. The darkened sides in the figure are the edges of the roof. This trim
will be painted white. Find the length of each of these two sides of
the triangle.
36°
36°
17 m
b. The inside of the triangle will be painted red. Find the area of the
red triangle.
8. Angie has 40 meters of fencing to use to create a safe play area for her baby brother. She wants to
make the play area in the shape of a triangle, so she builds it as shown below.
a. Is this a right triangle? Justify your answer.
C
16 m
b. Find the measure of each angle.
12 m
B
12 m
A
9. Does the Law of Sines and Law of Cosines work on a right triangle? Would you use it on a right
triangle? Why or why not.
Teacher Notes:
 These problems came from two places:
Math Connections 2a p269
Contemporary Mathematics in Context Assessment Resourse 3A p7-12
These books have more problems/assessments we could use. Also, I didn’t touch the INT 3
book/practice bank/assessment.


Pictures are available- But I’m not putting them in for #’s 1,2,4,6
I will copy and insert pictures as follows:
#3- math conn p 269 # 3
#5- Contemporary p 7 #1
#7 – Contemporary p 8 #4
#8- Contemp p 10 #1
#9- Contemp p 11 #3
Answers: (I’ll have to finish tomorrow when I have graphing calc.)
1- use Law of cosin
2- use Law of cosine
3- Use Law of Sine
4- a) use L of cos
5- Law of cos
b) use either
Answ: 118.4 yards
6- 2x law of cos OR cos, then law of sin Answer: m< A = 120
7- a) law of sin
Ans: 10.5m
8- 2x law of cos OR cos, then law of sin
m <B =
m<C=
b) use regular sine Ans: 52.5
Answer: No, pythag doesn’t work.
83.6,
,
9- Yes, but using them is not necessary, since sine, cosine, and tangent work in a right triangle.