Stitz-Zeager_College_Algebra_e-book

# We graph it below x2 x 2 y 2 xy 2 2 x y2 the

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: uares. 1 2 (a + b + c) = a+b+c 2. To 778 Applications of Trigonometry complete the proof, we note that (s − a) = = = Similarly, we ﬁnd (s − b) = a+c−b 2 a+b+c −a 2 a + b + c − 2a 2 b+c−a 2 and (s − c) = a+b−c 2. Hence, we get (b + c − a) (a + c − b) (a + b − c) (a + b + c) · · · 2 2 2 2 = (s − a)(s − b)(s − c)s A2 = so that A = s(s − a)(s − b)(s − c) as required. Example 11.3.3. Find the area enclosed of the triangle in Example 11.3.1 number 2. Solution. We are given a = 4, b = 7 and c = 5. Using these values, we ﬁnd s = 1 (4 + 7 + 5) = 8, 2 (s − a) = 8 − 4 = 4, (s − b) = 8 − 7 = 1 and (s √ c) = 8√ 5 = 3. Using Heron’s Formula, we get − − A = s(s − a)(s − b)(s − c) = (8)(4)(1)(3) = 96 = 4 6 ≈ 9.80 square units. 11.3 The Law of Cosines 11.3.1 779 Exercises 1. Use the Law of Cosines to ﬁnd the remaining side(s) and angle(s) if possible. (a) a = 7, b = 12, γ = 59.3◦ (f) a = 7, b = 10, c = 13 (b) α = 104◦ , b = 25, c = 37 (g) a = 1, b = 2, c = 5 (c) a = 153, β = 8.2◦ , (d) a...
View Full Document

## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online