Trig Applied Problems Putting trig ratios to work (5.7)

POD– back to right triangles Give the six trig values for β. β

Solving the triangle This means finding the lengths of all sides and measures of all angles. Today we’ll focus on right triangles, although at some point we’ll move to all types of triangles. Let’s round measurements of sides and angles to approximately equal precision. Sig. figs for sidesDegrees 2 1° 3.1° 4.01°

Solving the triangle Here’s a general triangle. How do the sides and angles match up in terms of greatest to least? How do you know? β α γ A B C c a b

Solving the triangle Solve ΔABC given β = 90°, α = 34°, and b = 10.5 β A B C c a b

Solving the triangle This skill is used in surveying and elevation work. Look at example 4, on page 442. Try it at tables first!

Solving the triangle It’s also used in navigation. You’ll see the word “bearing,” which gives the direction east or west off of a north/south axis. Look at example 5 page 444. How far apart are the ships after an hour?

Solving the triangle To determine the bearing from ship B to ship A, draw a north/south axis off ship B.

Trig functions We can move past triangles and put the trig functions to work. Look at the handout with annual daylight hours in four cities. We’ll focus on Anchorage, AK. When we’re done, graph the equation on graphing calculators to verify.