5 Find the indicated angle or side Give an exact answer 5 Fi

5) Find the indicated angle or side. Give an exact answer 5) Find the exact length of side a. B) 1 13 6) Find the measure of angle A in degrees. A) 60 B) 120 135 D) 140 Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. 7) B- 63 30 a -12.2f c-7.8 ft 7 A) b 12.2 ft, A 75 07, C 41 23 b 13.2 ft, A -73 07, C-3723 B) b 11.2 ft, A-77 49, C-38 41 D) No triangle satisfies the given conditions. Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. 8)a=153 m b 161 m c= 171 m 8) A) 722 m2 B) 14,058 m2 11,246 m2 D) 16,869 m2 Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°1. 9)(-16, A) 256; 180 8) 16: 180 ) 16; 270 D) 16;90 10) (63,8 10) A) 16;30 B)16 /2;60 32;30 D) 16; 150 Find the component form of the indicated vector 11) Let u--3), vr(-6,4). Find u-v A) (9,-10) Write the vector in the form ai+ bj A) 6i-5j B) (2,3) D) (12,-7) 12) (-56) 12)

Solution

5) c² = a² + b² - 2abcos45 = 25 + 18 - 2 x 5 x 3sqrt(2) x 1/sqrt(2) = 13

=> c = sqrt(13) (option C)

6) (2sqrt(13))² = 2² + 6² - 2 x 2 x 6cosA

=> 52 = 4 + 36 - 24cosA

=> cosA = -0.5

=> A = 120^o (option B)

7) b² = a² + c² - 2accosB = (12.2)² + (7.8)² - 2 x 12.2 x 7.8 x cos(63^o30\') = 124.7596

=> b = 11.2 ft

^a2 = b² + c² - 2bccosA => (12.2)² = (11.2)²+ (7.8)² - 2 x 11.2 x 7.8 x cos(A) => A = 77^o49\'

=> C = 180 - 63^o30\' - 77^o49\' = 38^o41\'

8) A = sqrt(s(s-a)(s-b)(s-c))

s = (a+b+c)/2 = (153 + 161 + 171)/2 = 242.5

A = sqrt(242.5 x 89.5 x 81.5 x 71.5) = 11246.0294 m²

9) 16, 180^o

10) magnitude = sqrt((8sqrt(3))² + 8²) = 16

angle = tan^-1(8/8sqrt(3)) = 30^o

11) u - v = <6+6,-3-4> = <12,-7>

12) -5i^ + 6j^