It's your turn on trigonometry by triangles

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf file below.

Exercise 1.

Assume a triangle (ABC) with sides (a), (b), (c) has (b=2sqrt 3), (c=6) and the angle in (B) equal to (30^o). What could be its area?

Exercise 2.

Lina is watching the Empire State Building. Between her and the skyscraper there is a tree whose height is approximately equal to 3 meters. She notices that the top of the tree and the top of the skyscraper are on the same line of sight (the line from the eye of Lina and the top of the tree or of the skyscraper):

The distance between Lina and the tree is equal to 5 meters; the distance between the tree and the base of the skyscraper is equal to 1455 meters. Which is the height of the skyscraper if Lina is 1.70 meters high?