Chapter 4: Applications of Right Triangle Trigonometry

Warm-up 1.Find the angle between the diagonal of a cube and the diagonal of the face of the cube. 2.Two ladders, one of which is twice as long as the other, rest on the floor and reach the same vertical height on the wall. The shorter ladder makes an angle of 60 degrees with the floor. What angle does the longer ladder make with the floor? 3.Find the distance between the two cities given their latitude (assume one city is due north of the other):Johannesburg 26 o 10’ S Jerusalem31 o 47’ N

Solving a Right Triangle What does it mean to “solve” a triangle?

Example

Trigonometry and Bearings Bearings Air Navigation

Examples 1. A ship leaves port at noon and heads due west at 20 knots per hour. At 2 p.m., the ship changes course to N 54 o W. Find the ship’s bearing and distance from the point of departure at 3 pm.

Examples 2. A boat travels at 35 mph for 2 hours on a course N 53 o E, then changes to a course N 143 o E and travels for another 3 hours. Determine the distance from the boat to its homeport. What is the boat’s bearing from the boat’s homeport to its location at the end of 5 hours?

Examples 3. A sailboat leaves a pier and heads due west at 8 knots. After 15 minutes the sailboat tacks, changing course to N 16 o W at 10 knots. Find the sailboat’s bearing and distance from the pier after 23 minutes on this course.