SLIDE 1
Distance to the Moon
Bochum, Germany Donaueschingen, Germany
Lesson 3.1: Law of Sines Distance to the Moon Donaueschingen, - - PowerPoint PPT Presentation
Lesson 3.1: Law of Sines Distance to the Moon Donaueschingen, - - PowerPoint PPT Presentation
Lesson 3.1: Law of Sines Distance to the Moon Donaueschingen, Germany Bochum, Germany If ABC is a with sides a, b, & c, then B B a h c C b A a c h a b c = = Sin A Sin B Sin C C b A 20 b Ex 1: Solve the . b =
SLIDE 2
SLIDE 3
If ABC is a Δ with sides a, b, & c, then
A B C a b c h A B C a b c h
a Sin A b Sin B c Sin C = =
SLIDE 4
Ex 1: Solve the Δ.
A B C a=20 b c 30° 45°
b =
mC = 180 – (30 + 45)
= 180 – 75 = 105°
20 30 45 sin sin
b b 20 45 30 sin sin
b 2828 .
c =
20 30 105 sin sin
c c 20 105 30 sin sin
c 3864 .
SLIDE 5
Ex 2: Find the height of the pole.
8° 43° B C A a 22 ft b
a Sin A c Sin C
=
a sin sin 43 22 39
39°
a 22 43 39 sin sin
a feet 2384 .
SLIDE 6
If 2 sides and 1 opposite angle are given, then 3 possibilities exist:
- 3. 2 distinct Δs exist
WARNING! WARNING! DANGER, Will Robinson! DANGER!
- 1. No Δ exists
- 2. 1 Δ exists
(see book, p.280)
SLIDE 7
Ex 3: Show that there is no Δ for which a = 15, b = 25 and mA = 85°
A C B 25 15
15 85 25 sin sin
B
85°
sin sin B 25 85 15
sin . B 1660324497
> 1, outside range of sine and no Δ exists.
See p.280 & 281 for other examples.
SLIDE 8
419,171.4 km
Distance to the Moon
Bochum, Germany Donaueschingen, Germany 52.6997⁰ 52.7430⁰ 398 km