Mr. Giuseppe Cammarata at the Liceo Scientifico Statale Benedetto Croce in Palermo, Italy is using this material in his Course IV F. Many of the solutions below were written by his students.

3. a) Since the triangle is 45^o, 45^o, 90^o, it follows that the relationship of the sides of the isosceles triangle is We have k = 3 in this case, so v is (4.24 in decimal form).

b) Since the triangle is 30^o, 60^o, 90^o, it follows that the relationship of the sides is So the solution is 2k = 11, so k is 5.5 and v is (9.53 in decimal form).

c) This triangle is also 30^o, 60^o, 90^o, but we have the shorter side is 4. So from the previous relationship the hypotenuse v is equal to 8.

d) In this triangle we have only the right angle and so we can't apply the triangle's relationship. We apply the theorem of Pythagoras because we know the measure of two sides, so v is ( 5.74 in decimal form).

Solution by Gianluca Ridulfo and Sandro Caracausi.
Liceo Scientifico Statale Benedetto Croce, April 2001.