CS 121 – Quiz 3 Questions 4 and 5

Question 4 Let’s generalize the problem:

Given a tower of height H, on a hill sloping at angle a, with guy wires tied down at a distance D on either side of the tower, how long are the guy wires L and R? L and R each form the side of a triangle of which the lengths other two sides are known, and the angle between them can be easily calculated. Let’s find the angles first. Angle a is one angle in a right triangle, so the unknown angle must be (90 – a), and therefore so is angle r, leaving angle l to be (180 – (90 – a)), or just (90 + a).

Now that we know two sides of each triangle and the angles between them, we can easily find the unknown sides using the Law of Cosines: L^2 = H^2 + D^2 – 2*H*D*cos(l) R^2 = H^2 + D^2 – 2*H*D*cos(r) Remember that Maple expects the parameter given to cos() to be in radians, not degrees.

Question 5 Because there are 3 different versions of the same problem in this question, it makes sense to make a re-usable script. We can even re-use some of the script we wrote for Lab 3 Part 1. Let’s first identify the parameters: – T[i] – the body’s initial temperature – T[a] – the room’s temperature – T – the time taken to process the scene – B(t) – the body temperature after the scene has been processed

Given those parameters, we can easily plug them into the given equation and solve for k. Now that we have k, we can find the time of death. We know the following: – k – we just calculated this – T[i] – living body temperature (98.6 degrees F) – T[a] – the room’s temperature – B(t) – the first measured body temperature Given this, we can easily plug them into the given equation and solve for t.