Transcript 7.1 Law of Sines Day 1

7.1 Law of Sines
Day 1 Tues Feb 10
Do Now
Let Triangle ABC be a right triangle
where angle C is 90 degrees, angle B
is 37.1 degrees, and side BC is 6.3
Solve the triangle
Quiz Review
• Retakes by
Solving Triangles
• To solve a triangle means to find the lengths
of all its sides and the measures of all its
angles
• We’ve solved right triangles previously
Oblique Triangles
• A triangle that is not a right triangle is
considered oblique
• Oblique triangles can be solved if at least one
side and any other 2 measures (length or
angle) are known
Law of Sines
• Proof
Law of Sines
• In any triangle ABC,
sin A sin B sinC
=
=
a
b
c
Where side a is opposite of angle A, etc
Law of Sines notes
• When solving triangles, there is a possibility
that you can have one solution, two solutions,
or no solution.
• This depends on the equations you set up
– Remember, the range of sinx is [-1, 1]
Ex1
• In triangle EFG, e = 4.56, E = 43deg, G = 57 deg
• Solve the triangle
Ex3
• In Triangle QRS, q = 15, r = 28, Q = 43.6 deg
• Solve the triangle
Ex 4
• In triangle XYZ, x = 23.5, y = 9.8, X = 39.7 deg
• Solve the triangle
Ex5
• In triangle ABC, b = 15, c = 20, B = 29 deg
• Solve the triangle
Closure
• Solve the triangle ABC, if possible
• A = 131 deg, C = 23 deg, b = 10
• HW: p.608 #1-15 odds
7.1 Law of Sines
Day 2 Wed Feb 11
• Do Now
• In triangle ABC, B = 115deg, c = 45.6 yd, b =
23.8 yd. Solve the triangle
HW Review: p.608 #1-15
Ex2
• In book
Area of a Triangle
• Using the law of sines, we can find the area K
of a triangle
K = 12 bcsin A = 12 absinC = 12 acsin B
Ex6
• A university landscaping architecture
department is designing a garden for a
triangular area in a dormitory complex. Two
sides of the garden, formed by the sidewalks
in front of buildings A and B, measure 172 ft
and 186 ft respectively, and together form a
53 degree angle. The third side of the garden
measures 160 ft. Find the area of the garden
to the nearest square foot.
Closure
• Find the area of the triangle ABC given C =
75.16 degrees, a = 1.5 m, b = 2.1 m
• HW: p.608 #17-31 odds