What is the height of a tree if a man standing 5 feet tall is 42 ft from the tree and sees the top of the tree at an angle of elevation of 32°?

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?

Solve the system. -a+4b+2c=-8 3a+b-4c=9 b=-1 a.(0,11) ,-1,2) c.(1,1,-2) d.(2,-1,-1)

Suppose you want just guess at the answers in a 5 question multiple-choice test. each question has 3 responses and only one is correct. what is the probability of getting two questions right just guessing? 20 points 0.3275 0.2753 0.7532 none of the above