Name:
Pre-Calculus Honors
Do Now Unit 8 Lesson 6
Find the area of regular nonagon inscribed in a circle with a radius of 12 inches.
Name:
Pre-Calculus Honors
Do Now Unit 8 Lesson 6
Find the area of regular nonagon inscribed in a circle with a radius of 12 inches.
Station 1: Solving an oblique triangle
Given
a.)
a =10cm
c = 5cm
B =10°
Diagram
Draw a diagram and use the diagram to
describe the case you have.
b.)
a  12cm
A  50
B  35
How many triangles?
How many triangles can be formed with these given
dimensions?
Solve the triangles
Solve for the missing angles and sides of
the triangle(s).
Station 2: Solving an oblique triangle
Given
a.)
a =12cm
b = 31cm
A = 20.5°
Diagram
Draw a diagram and use the diagram to
describe the case you have.
b.)
a  15cm
b  25cm
A  85
How many triangles?
How many triangles can be formed with these given
dimensions?
Solve the triangles
Solve for the missing angles and sides of
the triangle(s).
Station 3: Applications of Law of Sines and Cosines #1
VERBAL
Find the area of regular nonagon circumscribed about a circle with a radius of 10 inches.
Part A.
Draw a diagram what represents the verbal.
Part B.
Find the area of the nonagon.
Station 4: Applications of Law of Sines and Cosines #2
VERBAL
A pole is tilted 8 degrees from the vertical and it casts a 22 foot shadow. The angle of elevation from the tip of
the shadow to the top of the pole is 43 degrees. What is the length of the pole?
Part A.
Draw a diagram what represents the verbal.
Part B.
What is the length of the pole?
Station 5: Applications of Law of Sines and Cosines #3
VERBAL
A hot air balloon is seen over Tucson Arizona, simultaneously by two spotters at points A and B that are
1.2 miles apart on level ground and in line with the balloon. The angle of elevation from spotter A to the
balloon is 68 degrees and the angle of elevation from spotter B to the balloon is 84 degrees.
Part A.
Draw a diagram what represents the verbal.
Part B.
How far is observer A from the top of the balloon?
Part C.
How far is observer B from the balloon?
Part D.
What is the altitude of the balloon in feet?
Station 6: Applications of Law of Sine and Cosine #4
VERBAL
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 18.4 degrees and 20.7 degrees.
Part A.
Draw a diagram what represents the verbal.
Part B.
Find the air distance the plane must travel until touching down on the near end of the runway in
feet.
Part C.
Find the ground distance the plane must travel until touching down on the near end of the runway
in feet.
Part D.
Find the altitude of the plane when the pilot begins descending in feet.
Station 7: Area and Oblique Triangles
1
1. Area = bh
2
2. The area of any triangle is one half the product of the lengths of the two sides times the sine of their
included angle. That is,
1
1
1
Area = bcsin A , Area = absinC , Area = acsin B
2
2
2
3. The law of cosines can be used to establish the following formula for the area of a triangle. This
formula is called Heron’s Area Formula.
Given any triangle with side lengths a, b, and c, the area of the triangle is given by
a+b+c
2
The Bermuda Triangle is the triangular region defined by San Juan, Puerto Rico; Miami,
Florida; and Bermuda. Using a map, determine the dimensions of the Bermuda Triangle.
Calculate the area that the Bermuda Triangle occupies in the Atlantic Ocean in square
miles.
Area = s(s - a)(s - b)(s - c) where s =
Summary: Can the above formulas be used to find the area of any triangle? Explain the advantages and
disadvantages of using one formula over another.
Station 8: Applications of Law of Sines and Cosines #5
VERBAL
A parallelogram has sides of 8 inches and 5 inches, and an angle of 110 degrees.
Part A.
Draw a diagram what represents the verbal.
Part B.
Find the area of the parallelogram.
Part C.
Find the length of both diagonals.
Name: ___________________________________________________________
Pre-Calculus Honors Unit 7 Station Lab
Station Final Answer
#
1
a.)
b.)
2
a.)
b.)
3
A.)
B.)
Key Notes/
Reminders/Formulas
Used
4.
A.)
B.)
C.)
5.
A.)
B.)
6.
7.
C.)
D.)
A.)
B.)
C.)
D.)
8.
A.)
C.)
B.)