Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.3 Investigating the Sine Law

6.3 Investigating the Sine Law Goals for Today: Learn one of the ways that we can find unknown sides and angles in a non-right angle triangle

6.3 Investigating the Sine Law Minds On: Sine Law Investigation textbook p.546 I will handout graph paper and protractors What conclusion do you draw?

6.3 Investigating the Sine Law If we have a non-right angle triangle, we can’t use the primary trig ratios to find an unknown side or angle In this case*, we can use the Sine Law to solve for an unknown angle or side if we are given: 2 sides and one angle across from a known side, or 2 angles and any side *The Sine law will work in right angle triangles

6.3 Investigating the Sine Law The Sine Law is: use this if solving for a side The small letters represent sides The large letters represent angles You work with two out of the three ratios

6.3 Investigating the Sine Law The Sine Law is also: use this if solving for The small letters represent sides The large letters represent angles You work with two out of the three ratios

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side A C B 29.5cm 44° 37.1cm Ex. 1 Find angle C

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side A C B 29.5cm 44° 37.1cm Ex. 1 Find angle C Angle B is across from a known side...

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 1. Find angle C in triangle ABC As with similar triangles, we need 3 out of 4 to be able to find the missing side or angle

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 1. Find angle C in triangle ABC As with similar triangles, we need 3 out of 4 to be able to find the missing side or angle

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

Humour Break

6.3 Investigating the Sine Law – Given 2 Angles and any Side X Z Y z=3 cm y x 88° 25°

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 2. Find side x and find side y in triangle XYZ *Found missing angle by using 180° rule

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 2. Find side x and find side y in triangle XYZ *Found missing angle by using 180° rule

6.3 Investigating the Sine Law – Given 2 Angles and any Side

and

6.3 Investigating the Sine Law – Given 2 Angles and any Side

6.3 Investigating the Sine Law – Given 2 Angles and Any Side A C B b 72° 43° 27.2cm a Ex. 3 Find the length side a and side b

6.3 Investigating the Sine Law – Given 2 Angles and any Side Ex. 1. Find side a and find side b in triangle ABC

6.3 Investigating the Sine Law – Given 2 Angles and any Side Ex. 1. Find side a and find side b in triangle ABC *Found missing angle by using 180° rule

6.3 Investigating the Sine Law – Given 2 Angles and any Side and

6.3 Investigating the Sine Law – Given 2 Angles and any Side

Homework Monday, January 6 th - Hwk p.549, #1-4, 6-10, 14 & 15