Applications & Models

MATH 109 - PrecalculusS. Rook

Overview

• Section 4.8 in the textbook:– Solving right triangles– Bearing

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Solving Right Triangles

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°

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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

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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 mb) a = 62.3 cm, c = 73.6 cm

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Solving Right Triangles (Example)

Ex 2: The height of an outdoor basketball backboard is 12.5 feet and the backboard casts a shadow 17.33 feet long. Find the angle of elevation of the sun.

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Bearing

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

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Bearing (Continued)

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Bearing (Continued)

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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.

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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?

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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?

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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)

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