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Right Triangle Trigonometry Activity We name the sides of a right triangle in relationship to one of the non-90° angles, θ: OPPOSITE (the leg furthest from the marked angle) ADJACENT (the leg next to the marked angle) HYPOTENUSE (the side furthest from the right angle) New definitions for the trig function: sine cosecant opp sin( ) hy p csc( ) cosine secant adj cos hy p sec( ) tangent cotangent sin( ) opp tan cos( ) adj cot( ) 1 hy p sin( ) opp 1 hy p cos( ) adj 1 adj tan( ) opp You can use the inverse of sine - written as sin-1(x) or as arcsin(x) - to find an angle if you know the sides called opposite and hypotenuse on the triangle. sin() (the angle) -1 OPP sin (HYP ) Similarly, cosine and tangent have inverses. Advice for rounding numbers in this class and all math classes: never round a number before the end of a problem -- it leads to errors! In-Class Examples: Solve the following triangles (use exact values until the last calculation wherever possible, round answers to the nearest hundredth): 90 cm o 20 8 ft 35 o 540 in. 90 in. Right Triangle Trig Problems: (18 points) NAME For each triangle, solve for all the missing sides and angles. All angles are in degrees. Make sure you use the degree symbol, appropriate units, and round to the nearest 100th. Show work to the right side. Write the answers in the appropriate location on each triangle: WORK: 25 cm (1) o 39 (2) 14 cm 11 cm (3) 2.31 m o 20 (4) 90 cm 540 cm (5) 65" 72" (6) 120 cm o 65 h= This is an isosceles triangle. Also find h, the height