Download NEW: Solving Triangles That Are Not Right

Mrs. Scott
Honors Trig/Pre-Calc
Name:_________________________________
Date:__________________________________
6.1 – Law of Sines
Objectives:
1. Use the Law of Sines to solve oblique triangles.
2. Use the Law of Sines to model and solve real-life problems.
3. To find the area of oblique triangles.
Question?: How do you solve a triangle for lengths of sides and measures of angles if it is not a right triangle?
Before:
Given two measures of a right triangle all the other measures can be found.
Find the measures of the missing sides and angles.
A
49O
c
b
C
B
7
B=
b=
c=
NEW: Solving Triangles That Are Not Right: Known as ________________________.
C
sin A =
b
a
sin B =
h
solve each for h.
h=
A
c
B
h=
thus
=
rewritten as…
Law of Sines
=
Examples: Solve for all missing sides and angles (problems 1 and 2). Then, thinking back to Geometry
what information are you given (AAA, ASA, AAS, etc.)?
1. Given angle A = 30°, angle B = 45°, and side b = 32 feet. Find the remaining sides and angles.
E
2.
f
d
96
23
D
30
F
3. The course for a boat race starts at point A and proceeds in the direction South 52 West to point B, then in
the direction South 40 East to point C, and finally back to point A. Point C lies 8 kilometers directly south of
point A. Approximate the total distance of the race course.
*Note: Use Law of Sines when given ______ or ______.
**Strategies for checking your work. In a triangle the largest angle is across from the ____________ side. The
smallest angle is across from the _________________ side.
The ambiguous case: Given SSA there may be more than one possible outcome.
Given sides a and b, and angle A.
SSA: a < h where h = height of triangle
SSA: a = h where h = height of triangle
b
b
A
A
# of Possible Triangles =
SSA: a > h but a < b
# of Possible Triangles =
SSA: a > h and a > b
b
b
A
# of Possible Triangles =
A
# of Possible Triangles =
How will you know if there are no solutions?
Show that there is no triangle for which B=58°, a = 5, and b = 3.4.
How will you know if there is one solution?
Show that there is one solution for a triangle in which A=41°, a = 24, and b = 10.
How will you know if there are two solutions? (Only check for when given ______)
Show (and find) that there are two solutions for a triangle in which A = 32°, a = 6.5, and b = 9.2.
*Note: Use Law of Sines when given ______, _______, or ______.
Law of Sines Practice
1. In triangle EFG, e = 4.56, E = 43°, and G = 57°. Solve the triangle for all values.
2. In triangle ABC, b= 24, A = 121°, and C = 21°. Solve the triangle for all values.
3. In triangle ABC, a = 15.6 in., A = 89°, and b = 18.4 in. Solve the triangle for all values.
4. In triangle ABC, A=36.5°, a = 24, and b = 34. Solve the triangle for all values.
5. In triangle ABC, a = 20.01 cm, b= 10.07 cm, and A = 30.3°. Solve the triangle for all values.
6. Two observers are standing on shore ½ mile apart at points A and B and measure the angle to a sailboat
at a point C at the same time. Angle A is 63° and angle B is 56°. Find the distance from each observer
to the sailboat.
7. Find the area of the triangle having the indicated angle and sides.
a. C = 110°, a = 6, b = 10
b. B = 130°, a = 92, c = 30