Need help asap 30 points Often times you can use similar triangles in the real
world. Sarah is attempting to find the height of a tree
by using a mirror. By the laws of physics, she knows
that the angle of incidence is congruent to the angle of
reflection (these are marked in red on the diagram).
Explain why the two triangles are similar and if she
knows her height and the distance from the mirror to her
feet and also the distance from the mirror to the tree
how could she calculate the height of the tree?

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?

Scores on a university exam are normally distributed with a mean of 78 and a standard deviation of 8. the professor teaching the class declares that a score of 70 or higher is required for a grade of at least “c.” using the 68-95-99.7 rule, what percentage of students failed to earn a grade of at least “c”?

Alice is paying her bill at a restaurant. but tax on the cost of a male is 5%. she decides to leave a tip 20% of the cost of the meal plus the tax