aim: what is the law of sines and what good is it, anyway?
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Aim: What is the Law of Sines and what good is it, anyway?. The length of each of the equal sides of an isosceles triangle is a and the measure of a base angle is 15 o . Express the area of the triangle in terms of a. Do Now:. Deriving the Law of Sines. The Law of Sines. - PowerPoint PPT PresentationTRANSCRIPT
Aim: Law of Sines Course: Alg. 2 & Trig.
Aim: What is the Law of Sines and what good is it, anyway?
Do Now:
The length of each of the equal sides of an isosceles triangle is a and the measure of a base angle is 15o. Express the area of the triangle in terms of a.
Aim: Law of Sines Course: Alg. 2 & Trig.
Deriving the Law of Sines
Area of ABC
12
ab sinC 12
ac sinB 12
bc sinA
sinCc
sinB
b
sinAa
The Law of SinesUsed to find the measure of a side of atriangle when the measures of two anglesand a side are known (a.a.s. or a.s.a.).
csinC
b
sinB
asinA
Aim: Law of Sines Course: Alg. 2 & Trig.
Finding a Length
In ∆ABC, a = 10, mA = 30, and mB = 50.Find b to the nearest integer.
Law of Sines
solve proportion:
csinC
b
sinB
asinA
bsin50
10
sin30
bSin30 = 10sin50
b 10sin50sin30
b = 15.32088886To nearest integer, b = 15
Aim: Law of Sines Course: Alg. 2 & Trig.
Model Problem
In ∆DAT, mD = 27, mA = 105, and t = 21.Find d to the nearest integer.
solve proportion:
Law of Sines
csinC
b
sinB
asinA
21sin48
d
sin27
dSin48 = 21sin27
d 21sin27sin48
d = 12.82899398
To nearest integer, d = 12
tsinT
d
sinD
Establish ratiosbased on problem:
D
A
Tt =21 105º
27º 48º
Aim: Law of Sines Course: Alg. 2 & Trig.
Model Problem
In ∆ABC, a = 12, sinA = 1/3, and sinC = 1/4.Find c.
Solve proportion:
Law of Sines
csinC
b
sinB
asinA
c14
1213
1/3c = 3
c = 9
csinC
a
sinAEstablish ratiosbased on problem:
Aim: Law of Sines Course: Alg. 2 & Trig.
Model Problem
In ∆ABC, mB = 30 and mA = 45.Find the ratio a : b.
Solve proportion:
Law of Sines
csinC
b
sinB
asinA
bsin30
a
sin45
bsinB
a
sinAEstablish ratiosbased on problem:
b12
a2
2
Aim: Law of Sines Course: Alg. 2 & Trig.
Model Problem (con’t)
In ∆ABC, mB = 30 and mA = 45.Find the ratio a : b.
b12
a2
2
Simplify:
22
b 12
a
2212
ab
21
ab
Aim: Law of Sines Course: Alg. 2 & Trig.
Model ProblemIn right triangle ABC, mC = 90 and mA = 56, and BC = 8.7. Find AB to the nearest tenth.
C A
B
c
b
8.756º
csinC
a
sinAEstablish ratiosbased on problem:
csin90
8.7
sin56
Solve proportion:
c sin56 8.7sin90
c 8.7sin90
sin56
c = AB
10.49409615
To nearest tenth, d = 10.5
Aim: Law of Sines Course: Alg. 2 & Trig.
Regents Prep
Triangle ABC is an isosceles triangle. Its base is 16.2 cm. and one base angle is 63o20’. Find the length of one of the congruent sides to the nearest hundredth of a cm.
17.97 cm
Aim: Law of Sines Course: Alg. 2 & Trig.
Model Problem
A surveyor at point P sights two points X and Y that are on opposite sides of a lake. If P is 200 m. from X and 350 m. from T, and mXPY = 40, find the distance from X to Y to the nearest meter.
Aim: Law of Sines Course: Alg. 2 & Trig.
The Product Rule