91Ó°ÊÓ

a Find the ratio of the longer leg to the hypotenuse in a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle. b Find the ratio of one of the legs to the hypotenuse in a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle.

The legs of an isosceles triangle are each \(18 .\) The base is 14 a. Find the base angles to the nearest degree. b. Find the exact length of the altitude to the base.

Prove that the diagonals of a square are congruent and perpendicular.

One diagonal of a rhombus makes an angle of \(27^{\circ}\) with a side of the rhombus. If each side of the rhombus has a length of 6.2 in., find the length of each diagonal to the nearest tenth of an inch.

Find the perimeter of trapezoid \(\mathrm{ABCD}\), in which \(\overline{\mathrm{CD}} \| \overline{\mathrm{AB}}\), \(\cos \angle \mathrm{A}=\frac{1}{2},\) and \(\mathrm{AD}=\mathrm{DC}=\mathrm{CB}=2\).

Mary and Larry left the riding stable at 10 A.M. Mary trotted south at 10 kph while Larry galloped east at 16 kph. To the nearest kilometer, how far apart were they at \(11: 30 ?\)

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

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)

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

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.