⦁ The Occupational Safety and Health Administration (OSHA) sets standards for a variety of occupations to help prevent accidents and other safety hazards. OSHA’s standard for the angle formed by a ladder and level ground is 75°. The same 10-ft long ladder is placed against the building according to OSHA’s safety standard. What is the distance between the foot of the ladder and the foot of the building? Round your answer to the nearest tenth. Show your work

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

How do your peer relationships affect your overall health status? what can you do to improve your peer relationships?

In a small section of a stadium there are 40 spectators watching a game between the cook islands and fiji. they all support at least one of the two teams. 25 spectators support the cook islands and 16 of these support both teams. how many support only fiji?