Download Notes 8 - Garnet Valley School District

Notes 8.1 and 8.2- Law of Sines and Cosines
Algebra III Honors
Date: _________
Goal:
Recall:
 Law of Cosines:

When to use:

Law of Sines:

When to use:
New Idea: The Ambiguous Case in the Law of Sines:
Consider the triangles below:
It seems as though the three parts we are given do not necessarily lock in the measures of the
other sides and angles. What order are the parts in (SSS, etc.)?
Was that an accepted way to prove two triangles congruent in Geometry?
How does this affect us when we solve for m  B?
Solve the following triangles
1) B = 55°40’, b = 8.94 m, and a = 25.1 m
2) A = 55.3°, a = 22.8 ft, and b = 24.9 ft
3) a = 9.47 ft, b = 15.9 ft, and c = 21.1 ft
4)
The pitcher’s mound on a women’s softball field is 43 feet from home plate and the
distance between the bases is 60 feet. (The pitcher’s mound IS NOT halfway between
home plate and second base) How far is the pitcher’s mound from first base?
5)
A ship travels 60 miles due east and then adjusts it course, as shown below. After
traveling 80 miles in this new direction, the ship is 139 miles from its point of departure.
Describe the bearing from point B to point C.
One More Formula:
 HERON’s Area Formula:
6)
Find the area of a triangle with side lengths 43 m, 53 m, and 72 m.
HW: p. 568 18, 26, 34, 44,52; p. 575 # 32 – 44 M4, 45, 52, 56
Notes 8.1 and 8.2 Day 2- Law of Sines and Cosines
Algebra III Honors
Name: _________
Date: _________
Skills check
1) Find the three angles of the triangle whose sides have lengths 6, 8, and 12.
2) Given A = 80 , b = 16, and c = 12, solve for the remaining angles and side of the
triangle
3) In a softball game, the batter hits a ball to dead center field, a distance of 240 feet from
home plate. The center fielder then throws the ball to third base and gets a runner out.
The distance between the bases is 60 feet. How far is the center fielder from third base?
4) Given a = 5, b = 9, and c = 8, find the area of the triangle.