Notes for Session 5, Part C

 Note 6 When considering an angle and the height-to-distance ratio formed by that angle, it is common to name the angle with a Greek letter. The first letter in the Greek alphabet is (alpha), the second letter is (beta), and the third letter is (gamma). In this session, we frequently refer to and .

 Note 7 Take your time working through the problems in order to make sense of the relationships, as future questions will build on what you learn here.

 Note 8 If you have not used a scientific calculator recently, first obtain the information in the table given in this section. On some calculators, you enter the angle measure (e.g., 46) and then press the tangent button to get the tangent ratio (e.g., 1.035530314). (Note that the data in the table have been rounded, in this case to 1.036.) What if you have the h/d tangent ratio and want to find the corresponding angle? In that case, you'd enter the ratio first (e.g., 1.036) and then press the inverse of the tangent key (e.g., tan-1), which is usually a "second" function, to obtain the angle measure (e.g., 46.01298288). This number can also be rounded.

 Note 9 Notice that this problem is not very different from what you did in Part A. Using a tangent ratio is a kind of shortcut. When you drew similar triangles and set up the proportion between the corresponding sides, you were really calculating the tangent ratio of the triangle with known dimensions, and you then used that to find the unknown length on the other triangle. Now you can calculate the same ratio without the middle step of drawing a similar triangle -- you just need to find the tangent of the angle and then use it in the equation.