Applications & Models MATH Precalculus S. Rook

Overview Section 4.8 in the textbook: – Solving right triangles – Bearing 2

Solving Right Triangles

We are now ready to solve for unknown components in right triangles in general: – ALWAYS draw a diagram and mark it up with the given information as well as what is gained while working the problem – When given two sides, we can obtain the third side using the Pythagorean Theorem – When given two angles, we can obtain the third angle by subtracting the sum from 180° 4

Solving Right Triangles (Continued) – When given one angle and one side, we can obtain another side via a trigonometric function SOHCAHTOA – When given two sides, we can obtain an angle via an inverse trigonometric function 5

Solving Right Triangles (Example) Ex 1: Refer to right triangle ABC with C = 90°. In each, solve for the remaining components: a) A = 41°, a = 36 m b) a = 62.3 cm, c = 73.6 cm 6

Solving Right Triangles (Example) Ex 2: The height of an outdoor basketball backboard is 12.5 feet and the backboard casts a shadow feet long. Find the angle of elevation of the sun. 7

Bearing

Bearing: the acute angle formed by first referencing the north-south line of a compass followed by a position east or west – 4 possibilities for bearing based on the 4 quadrants in the Cartesian Plane Used frequently in navigation and surveying 9

Bearing (Continued) 10

Bearing (Continued) 11

Bearing (Example) Ex 3: Leaving from port at noon, a boat travels on a course of bearing S 29° W, traveling at 20 knots (nautical miles per hour). a) How many nautical miles south and how many nautical miles west will the boat have traveled by 6 p.m.? b) At 6 p.m., the boat changes course to due west. Find the boat’s bearing and distance from port at 7 p.m. 12

Bearing (Example) Ex 4: A man wandering the desert walks 2.3 miles in the direction of S 15° W. He then turns 90° and walks 2 miles in the direction N 75° W. At that time, how far is he from his starting point and what is his bearing from his starting location? 13

Bearing (Example) Ex 5: A ship is 45 miles east and 30 miles south of port. The captain wants to sail directly to port. What bearing should be taken? 14

Summary After studying these slides, you should be able to: – Solve for all dimensions in a right triangle – Solve application problems involving right triangles – Apply the concept of bearing to solve right triangle problems Additional Practice – See the list of suggested problems for 4.8 Next lesson – Using Fundamental Identities (Section 5.1) 15