Math142

Summer 2000

Exam 2

 

  1. (16 pt) Find all possible triangles given the following data (S=side and A=angle).

a)           b)

 

2.      (14 pt) Consider a solid cube with each side of length x. Find the angle between the diagonal of the bottom face and the “super-diagonal” connecting the opposite two vertices.

 

  1. (20 pt) An astronomer on earth spots an asteroid when looking through his telescope at an angle of elevation of 63°. He immediately calls his friend on the space shuttle (which is 25,000 miles distant from him at an angle of 70°) and the shuttle reports that they observe the asteroid at an inclination of 61.5°. How far away is the asteroid (from the astronomer)?

 

  1. (16 pt) Find the area enclosed by the following triangles:

a)      With vertices at the points (0,0), (1,1), (-2,-3).

b)      With sides of lengths 5,12 and 10.

 

5.      (12 pt) Show that if you double the lengths of the sides of a given triangle, then you quadruple the area.

 

  1. (20 pt) A 60-foot long flagpole is on the top (edge) of a building. A recent windstorm has bent the pole so that it is now tilted at 30° from the vertical. An observer on the ground notices that that his angle of sight to the bottom of the pole is 50° and the angle to the top is 52.5°. How tall is the building?

 

  1. (12 pt) Draw a picture and state the law of cosines and the law of sines. (Be sure that you label everything clearly). Briefly explain the hazards of using the law of sines to determine angles.