Calendar: 1887-1888 Page 671

general literature and science 675 Divisions II IV -eudin VI anti XI Crigonometrp Prove that triangles on the same base are to one another as their altitudes Explain what is meant by saying that similar triangles are to one another in the duplicate ratio of their homologous sides If an angle of triangle be bisected by straight line which also cuts the base prove that the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base together with the square on the straight line which bisects the angle What is tetrahedron an octahedron and dodeca- hedron How many edges and how many solid angles have each of these solids Draw straight line perpendicular to two straight lines which are not in the same plane If the sun's altitude be 60 what angle must stick make with horizontal plane so that its shadow upon that plane may be the longest possible person having observed that the altitude of certain tower was 35 advances 80 yards nearer to it and then finds that the altitude is 70 Find the height of the tower The angles at the base of triangle are 45 and 30 and the height of the triangle is 100 inches Find the sides of the triangle Find the value of θ from the following equations tan30 tan2 tantf -1 91 ץ cos sin2 θ י sin20 co8 10 Find χ and from the equations sin χ siny cosjt cosy V2 Τ υ