Question

i need help with these 3 homework problems, thank you !

Solve a Triangle Using the Law of Sincs (SSA) Ambiguous Case Suppose that the measure of angle A and the lengths of sides a and b of a triangle are given. Depending on the length of side a (shown in red) relative to the length of the altitude h, we have four different scenarios No triangle One right triangle One oblique triangle Two triangles: One acute and one obtuse triangle В B B ας Sidea is too short to meet side c. Side a exactly equals the altitude. One triangle possible << Side a intersects side e at an obtuse or acute angle. 3. (No solution) Solve the triangle with 4 -28°, -12, and b = 38. Round the measures of the unknown angles and side to 1 decimal place. 4. (1 solution) Solve the triangle with C = 68°, b = 13, and e- 15. Round the measures of the unknown angles and side to 1 decimal place.

Answer 1

Given that LC = 609 6=13, and cais we find the unknown angle and sick use the sine formula Nou &inB finc 69" ar? SinB 7 &inc C A C.: 15 B SinB = 134.500 (68) 15 = S(0.9279395) 15 12:05339005' 13 SMB = 0.8035579 Sin' (0-803559) B - 53.471318° B = 53.5 Aug we know that the sum of three angle of triangle is 180 LAHLBtLo=1000 LA 180-( 53.5+68') LA = 1810°-121.59 KA = 58.5% Aug . Now sinA. Sinc c ce

a = a cx sind sinc 154 son(sas) sin (68°) 15% (0.05 26 4016) (0.92718395) : 12.7896024 (0.927181305) a 13 13.79403 13.8 Hence the value of unknown angle and sicke of the friongele ABC arer LA = 58.5" LB = 53.5" Ans a = 13.8

284 С = Solm; 3; Given that A-28 ° a= 12, b=38 Now use sime formula b= 38 SimA SimB B Sim A SimB b Simß = 38 Sim 28 " Sim 28°=0.46947158 12 ? 3.16666667 X 0.46947156 Sine b a e a=12 = 38 Sim28 = li48 .. 'Max the value of Sime is 1 Minimum value of Sime is - so Sim B = 1 Sym B = Sinq6 B = 90° Ang We know that the sum of three angle of a traingle is equel to 180° LA ELB+22=120 28+90+20=180° ze=120 – 118 I c = 62] Ang Now Sima Sime a C a sime Sim 12 x S 62° Sim28° 12 x 0.0021 0.4695 I

= 10.5852 0.4695 = 22.5456869 C = 22.5 Aus angle formula Sol": Solve the double " (as zo = 1a 28en?o ΟΥ Sim²0= |- Caso 2 I-Cosao 2 X-rtasimeo 2 Simeo - 1 tan²o Ittam?a = 2 to OR Coszoz Sim² o 2 A me Now Cos?o= It los ao cos 20= (264²6-11 2 It Cosao = x+ 2Caseo-t 2 2 & Cos²a 모 lf Cos ad 2 2 Cas?o Ang Now c 1- COS20 2 IHCosao tam?o= 1- Cos 20 It cos zo 1-(1- 284m²0) X+ 2 cos²ot . X-+2 Sino 2 Cos²o 2 Simeo 2coste

= Sinza costo Itlas 20 = fam?o 1 +26520 Solms. Given that Sinan Now Rewrite the Sim" an= 2 = (Sim22n)? I-eosun)? : Sen?n)= 1- Cosun It cosun - 2 Cosun u 1+ Itlason - 2 Cosun 2 И 2 tlt Casan-ucasun 2x4 3+ Casanulosun 2 N. Simano = Cason-u Cosunt 3