Grade Level: 9-12

Subject Area: Mathematics, Trigonometry

Goals: Broader: Introduction of tools for pythagorean geometry

Unit: Identification and elementary application of sine, cosine and tangent

Unit Performance: Students will develop, solve and Explain solutions to equations

Behavioral Objective: Given the length measures of two sides of a right triangle, these proportions can “prove” the length of the third (unknown) side with Pythagorean Theorem

Technology Benchmark: Flash movie with interactive progression control will allow students to retrace the progression of the procedure example.

SSS/CBC, FCAT Integration: Mathematics SSS: 3)Geometry and Spacial Sense M.A.D.3.4.1

Materials: Monitor Projector, Laptop, Dry-erase board and markers.

Development/Detail/Procedures:

Concept: SOHCAHTOA is an acronym used a mnemonic
device for recalling the ratios of proportion for a right triangle:

SOH : sine = opposite/hypoteneuse

CAH : cosine = adjacent/hyponteneuse

TOA : tangent = opposite/adjacent

The Pythagorean Theorem establishes proportions based on a proportional formula: a2+b2=c2

For instance,




If the cosine of a is 4/5 and it equals the sine of b(4/5) then the cosine of b, x/5, must equal the sine of a (x/5). If the tangent of b=4/x, then the tangent of a=x/4.
Applying Pythaforas, 16(4.4) +x (x+x) = 25 (5.5) and the answer is 9 (3.3) then it must follow that the following formula follows: sin a 4/5 x sin b 4/5 divided by hyp2/adj2 = x.

Procedures:

Intro: Present as a riddle: ask class how they can find the missing side of the triangle given only two. Accept proposals,then present Pythagorean Theorem (unless one or more student knows, then coach them through presentation), then cross check with SOHCAHTOA.
Solve example problems individually, calling on students to assist. Also have students assist in setting up problems. Have students volunteer to demonstrate/explicate procedute and solve problems before class.