91Ó°ÊÓ

PADIM is a regular square pyramid. Slant height PR measures \(10,\) and the base diagonals measure \(12 \sqrt{2}\). a Find ID. b Find the altitude of the pyramid. c Find RD. d Find PD (length of a lateral edge). (GRAPH CANT COPY)

Find the length of the apothem of a regular pentagon that has a perimeter of \(50 \mathrm{cm}\).

Two buildings are 100 dm apart across a street. A sunbather at point P finds the angle of elevation of the roof of the taller building to be \(25^{\circ}\) and the angle of depression of its base to be \(30^{\circ} .\) Find the height of the taller building to the nearest decimeter.

Find, to the nearest tenth, the perimeter of a quadrilateral with vertices \(\mathrm{A}=(2,1), \mathrm{B}=(7,3), \mathrm{C}=(12,1),\) and \(\mathrm{D}=(7,-4),\) and give the figure's most descriptive name.

Find the diagonal of a cube if each edge is \(2 .\) (GRAPH CANT COPY)

Given a trapezoid with sides \(5,10,17,\) and \(10,\) find the sine of one of the acute angles.

Show that the parallelogram whose vertices are \((-1,-3),(2,1)\) \((3,-2),\) and \((-2,0)\) is not a rhombus.

Given \(\triangle \mathrm{ABC}\) with \(\angle \mathrm{C}=90^{\circ}\), indicate whether each statement is true Always (A), Sometimes (S), or Never (N). a. \(\sin \angle A=\cos \angle B\) b. \(\sin \angle A=\tan \angle A\) c. \(\sin \angle A=\cos \angle A\)

Find the diagonal of a cube if the perimeter of a face is \(20 .\) (GRAPH CANT COPY)

An observer on a cliff 1000 dm above sea level sights two ships due east. The angles of depression of the ships are \(47^{\circ}\) and \(32^{\circ}\). Find, to the nearest decimeter, the distance between the ships.