Please solve the following problems and explain

1.

Solve triangle ABC if AA = 431, (1 = 182.7, and b = 249.4. sinB 2 (round answer to 5 decimal places) There are two possible angles B between 0" and 180" with this value for sine. Find the two angles, and report them so that 131 is the acute angle. 131 = O and 4.32 = D (round these and all remaining answers to 1 decimal place) Thus, two triangles satisfy the given conditions: triangle A13101 and triangle 24ng02. Solve the first triangle: 4413101 401 : D and Cl : Solve the second triangle: A23202 AC2 : D and 02 Z To find the distance across a river, a surveyor choose points A and B, which are 214 it apart on one side of the river. She then chooses a reference point C on the opposite side of the river and finds that LBAC z 84" and LABC z 54". A 2141? B v 0' 840 54 C NOTE: The picture is NOT drawn to scale. Approximate the distance from point A to point C. distance = ft Find the distance across the river. height = ft Enter your answer as a number; your answer should be accurate to 2 decimal places. To nd the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. 2.39 km NOTE: The triangle is NOT drawn to scale. distance = Enter your answer as a number; your answer should be accurate to 2 decimal places. Assume La: is opposite side a, AB is opposite side b, and if}! is opposite side c. Solve triangle ABC if AA 2 oz 2 384, b = 8.4 yd, and c = 13.7 yd. Using the Law of Cosines, a. % yd. Your answer should accurate to 2 decimal places. Using the Law of Cosines again, cos AB = cos B m Your answer should accurate to 5 decimal places. Thus, ,8 % . Your answer should accurate to 2 decimal places. cos AC 2 cos'y x Your answer should accurate to 5 decimal places. Thus, *7 m Your answer should accurate to 2 decimal places. Check by seeing if the total of the three angles is 180. Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than ACAB : 53.2". Find the distance across the lake from A to B. C 380]"? NOTE: The triangle is NOT drawn to scale. distance m it Enter your answer as a number; your answer should be accurate to 2 decimal places. Remember, even if you enter an answer rounded to a set number of decimal places, if you use that number in a future calculation, you should use all of the decimal places reported on your calculator! Solve triangle ABC if [A : 43.1", a : 188.9, and b : 243.3. 51113 : (round answer to 5 decimal places) There are two possible angles B between 0 and 180" with this value for sine. Find the two angles, and report them so that [Bl is the acute angle. 431 : and 132 : (round these and all remaining answers to 1 decimal place) Thus, two triangles satisfy the given conditions: triangle A13101 and triangle AngCg. Solve the first triangle: 1413101 101 : D and 01 : Solve the second triangle: .4ng02 402 : D and 02