Math 142

Summer 1999

Exam 2

1. (10 pt) Write the law of cosines and explain why it is a “generalization of the Pythagorean Theorem.”

2. (54 pt) The following data are possibilities for triangles. For each part, find one solution or explain why there is no triangle with this data (if there are two solutions, you need only find one, but explain why there is another).

S=side and A=angle

a) (S,S,S)=(12,10,17) b) (S,S,S)=(24,23,50) c) (S,A,S)=(7,60º,9)

d) (S,S,A)=(4,4,45º) e) (S,S,A)=(4,5,45º) f) (S,S,A)=(5,4,45º)

3. (12 pt) Assume that a plane comes in for a landing at a constant angle. For safety reasons, that angle should be no more than 3º. If the cruising altitude is 30,000 feet, how many miles (measured along the ground) away from touchdown should the plane begin its descent?

4. (12 pt) Two fire towers (A and B) 15 miles apart both spot the smoke of a forest fire. Tower A measures and finds that the smoke is on a line 80º from the line connecting the towers. Tower B measures and finds that the angle to be 65º. How far is the fire from each tower?

5. (12 pt) You stand at the bottom of a vertical cliff. At the top of the cliff grows a large fir tree and you discover that your line of sight to the top of the tree is 49.4º and your line of sight to the base is 48.7º. Your friend at the top tells you that the height of a mature fir tree is about 80 feet. Use these facts to estimate the height of the cliff.

6. (10 pt) Find the area of a triangle with the three sides of length 12,20, and 28.