University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2019
Views:

299

Pages:

3
Author:

contravavif

ACCEL. PRE-CALCULUS/TRIG 3 Name: KEY Date: 6.1 Law of Sines Review: Given two measures of a right triangle all other measures can be found by using SOH-CAH-TOA. 1. Find the measures of the missing sides and angles. (Round all answers to 2 decimal places) A 49 90 deg - 49 deg = 41 deg tan 49 deg = 7/b sin 49 deg = 7 C b Π b = 7/(tan 49 deg) C = 7 sin 49^ * C 41 b = 6.085 c = 9.275 7 B B = 41 deg * b = 6.09 * c = 9.28 Discovery: Solving Triangles That Are Not Right→ pg 489 b C h sin A = h/b sin B = solve each for h. h = b * sin A B h= (a * sin B)/(hus) b sin A reuriten an as.. = asin B ab (sin A)/a = (sin B)/b *Make sure calc is in Degree mocle! The Law of Sines: used to solve triangles that are not right. = b C a A B [Q]/(sin[A]) = [b]/(sin[B]) = [C]/(sin[C]) side lengths angles ROUND ALL ANSWERS TO 2 DECIMAL PLACES! CASE 1: Given 2 angles and 1 side AAS or ASA Find the 3rd angle (add 2 angles and subtract from 180 deg ) Use the found value to find the other missing sides Find the value of an angle and its corresponding side using the Law of Sines 1) B = 57.3 deg C = 78.2 deg b = 6.2 B A 445 6.2 a 782 Adds to ( 20 deg CASE 2: Given 2 sides and 1 angle (opposite one of the sides) ASS * OBTUSE ANGLE: 2 possibilities no solution one solution Examples: ASS obtuse B 2) A = 102 deg b = 5 a = 3 A 102 5 Ass obtuse 3 Øble side a should be the longest since A is the largest, but side b is larger than side a Calc gives a 3 b-5 opp can't be larger than hyp! c 3) A = 107% x = 17.2 c = 12.2 A 12.2 B 107 Ass obtuse 7.2 C B-11.2 (3sin 8)/3 = (5sin 102)/3 sin B = (5sin 102 deg)/3 3 sin 102^ * = 5/(sin B) B = arcsin((5sin 102 ^ n)/3) = sin^4 (1.63/1) C= arcsin((12.2sin 10 deg)/17.2) Rightarrow c=42.7r (7.2 * 0.5inC)/17.2 = 12.2 sin 10^ 7 ) 17.2 m .2 sin 10n^ bullet = 12.2 sin C^ bullet c = 42.31 deg 6.2/(sin 523) = alpha/(sin 44.5 deg) Lambda = 44.5 deg 6.2/(sin 57.3 deg) = c/(sin 78.2 deg) (c * sin 57.3 deg)/(sin 52.3 deg) = 6.2 sin 78.2 sin 57.3^ Rightarrow c=7.21 B = 30.29 deg L_{A} = 101 deg m.2 sin 10 * eta deg = b/(sin 30.29 deg) (b * sin - 107 deg)/(sin 107 deg) = 17.2.sin 30.29^ sin 107^ Rightarrow b=9.07 c = 7.21 c = 78.2 ^ v c = 12.2 B = 57 * 0.3 deg - b = 6.2 a = 5.16 1. Sip * 0.57 .3^ * sin 57.3 * 6.2 sin 44.5 sin 57.3^ * Rightarrow a=5.16 b = 9.07 c = L_{A} = 102 deg B =