A blue boat and a red boat are on the same side of a lake and are 18 miles apart. The blue boat is 30 miles from a lighthouse on the opposite side of the lake. The angle formed by the boats and the lighthouse, and whose vertex is at the blue boat, measures 120°. Find the distance from the red boat to the lighthouse. What is the angle made from the lighthouse to the two boats?

9514 1404 393

Step-by-step explanation:

The Law of Cosines can be used to find the distance from the red boat to the lighthouse.

  b² = l² +r² -2lr·cos(B)

  b² = 18² +30² +2·18·30·cos(120°) = 1764

  b = √1764 = 42

The distance from the red boat to the lighthouse is 42 miles.

__

The angle at the lighthouse can be found using the law of sines.

  sin(L)/l = sin(B)/b

  L = arcsin(l/b·sin(B)) = arcsin(18/42·sin(120°)) ≈ 21.79°

The angle between the boats measured at the lighthouse is about 22°.

answer: what is the conflict?

step-by-step explanation:

*what has happened to new york city?

*what is in the time capsule?

* what did the kidz see that gave them hope?

*what will they do with what they find?

* how will they save the city?

* what challenges will they face along the way?

*what big choice will they make at the climax of the story?

* what lesson do they learn at the end of the story?