1. Solving Right Triangles
Trigonometry
MATH 103
S. Rook

2. Overview Section 2.3 in the textbook: Solving simple right triangles
Solving more complex problems with right triangles

3. Solving Simple Right Triangles

4. Solving Simple 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°

5. Solving Simple 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

6. Solving Simple 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

7. Solving More Complex Problems with Right Triangles

8. Solving More Complex Problems with Right Triangles
More complex problems will contain multiple triangles and/or figures, but the process still remains the same:
ALWAYS draw and mark up a diagram!
Calculations may require multiple steps
Sometimes there is more than one way to arrive at the desired answer
Only way to become proficient is to practice!!!

9. Solving More Complex Problems with Right Triangles (Example)
Ex 2: The circle has a radius of r and center at C. The distance from A to B is x. If C = 65° and x = 22, find: a) r b) y

10. Solving More Complex Problems with Right Triangles (Example)
Ex 3: The distance from D to C is x. If A = 32°, angle BDC = 48°, and AB = 56, find: a) h b) x c) angle ABD

11. Solving More Complex Problems with Right Triangles (Example)
Ex 4: Each edge of the cube is 5 inches long. Find the measure of the angle formed by diagonals CF and CH:

12. Summary After studying these slides, you should be able to:
Solve problems containing right triangles
Additional Practice
See the list of suggested problems for 2.3
Next lesson
Applications (Section 2.4)