Solving Right Triangles Trigonometry MATH 103 S. Rook

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

Solving Simple Right Triangles

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°

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

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

Solving More Complex Problems with Right Triangles

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!!!

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

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

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:

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)