1. 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 15 o. Express the area of the triangle in terms of a.

2. Aim: Law of Sines Course: Alg. 2 & Trig. Deriving the Law of Sines The Law of Sines Used to find the measure of a side of a triangle when the measures of two angles and a side are known (a.a.s. or a.s.a.).

3. Aim: Law of Sines Course: Alg. 2 & Trig. Finding a Length In ∆ABC, a = 10, m  A = 30, and m  B = 50. Find b to the nearest integer. Law of Sines solve proportion: bSin30 = 10sin50 b = 15.32088886 To nearest integer, b = 15

4. Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem In ∆DAT, m  D = 27, m  A = 105, and t = 21. Find d to the nearest integer. solve proportion: Law of Sines dSin48 = 21sin27 d = 12.82899398 To nearest integer, d = 12 Establish ratios based on problem: D A T t =21 105º 27º 48º

5. 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 1/3c = 3 c = 9 Establish ratios based on problem:

6. Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem In ∆ABC, m  B = 30 and m  A = 45. Find the ratio a : b. Solve proportion: Law of Sines Establish ratios based on problem:

7. Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem (con’t) In ∆ABC, m  B = 30 and m  A = 45. Find the ratio a : b. Simplify:

8. Aim: Law of Sines Course: Alg. 2 & Trig. Model Problem In right triangle ABC, m  C = 90 and m  A = 56, and BC = 8.7. Find AB to the nearest tenth. C A B c b 8.7 56º Establish ratios based on problem: Solve proportion: c = AB To nearest tenth, d = 10.5

9. 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 63 o 20’. Find the length of one of the congruent sides to the nearest hundredth of a cm. 17.97 cm

10. 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 m  XPY = 40, find the distance from X to Y to the nearest meter.

11. Aim: Law of Sines Course: Alg. 2 & Trig. The Product Rule