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 Δ 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 Δ . b =    sin 30 sin 45 C  b  20 sin 45  sin 30 b a=20 b  2828 . 45 ° 30 ° 20 c B c  A c =   sin 30 sin 105 m  C = 180 – (30 + 45)  c  20 sin 105 = 180 – 75  sin 30 = 105 ° c  3864 .

a 22 Ex 2: Find the height of the pole.    sin 43 sin 39 a c = C Sin A Sin C  a  22 sin 43  sin 39 39 ° b  2384 a . feet a 8 ° 43 ° A B 22 ft

WARNING! WARNING! DANGER, Will Robinson! DANGER! If 2 sides and 1 opposite angle are given, then 3 possibilities exist: 1. No Δ exists 2. 1 Δ exists 3. 2 distinct Δ s exist (see book, p.280)

Ex 3: Show that there is no Δ for which a = 15, b = 25 and m  A = 85 ° 15 25  B  25 sin 85   sin sin 85 sin B 15 C B  1660324497 sin . 15 25  > 1, outside 85 ° range of sine and no Δ exists. B A See p.280 & 281 for other examples.

Distance to the Moon 251,502.8 mi 419,171.4 km x 52.6997 ⁰ 52.7430 ⁰ 398 km Donaueschingen, Germany Bochum, Germany Homework: p.284 #2-8 even + #14