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© The Visual Classroom Trigonometry: The study of triangles (sides and angles) physics surveying Trigonometry has been used for centuries in the study of: astronomy geography engineering
© The Visual Classroom A B C adjacent h y p o t e n u s e opposite
A B C adjacent opposite h y p o t e n u s e
A B C opposite adjacent h y p o t e n u s e
A B C opposite adjacent h y p o t e n u s e
A B C opp adj hyp SOHCAH TOA
© The Visual Classroom A B C 8 6 10 op p adj hy p SOH CAH TOA
© The Visual Classroom A B C 3 4 5 adj opp hyp SOH CAH TOA
© The Visual Classroom A B C 5 12 13 adj opp hy p SOH CAH TOA
© The Visual Classroom sin 21° = cos 53° = tan 72° = 0.3584 0.6018 3.0777 Use a calculator to determine the following ratios. Be sure your calculator is set to degrees.
© The Visual Classroom sin A = 0.4142 cos B = 0.6820 tan C = 1.562 A = sin -1 (0.4142) B = cos -1 (0.6820) C = tan -1 (1.562) = 24° = 47° = 57° Determine the following angles (nearest degree).
© The Visual Classroom Determine the following angles (nearest degree). sin A = cos B = tan C = A = sin -1 (0.5833) B = cos -1 (0.2666) C = tan -1 (1.875) = 36° = 75° = 62° = 0.5833 = 0.2666 = 1.875
© The Visual Classroom A B C Example 1: Determine side measure of A 8 cm opp ad j SOH CAH TOA 13 cm tan A = 0.6154 A = tan -1 (0.6154) A = 31.6°
© The Visual Classroom A B C Example 2: Determine side b 55º b 8 cm b = 8 tan 55° b = 11.4 cm b = 8 (1.428) opp ad j SOH CAH TOA
© The Visual Classroom P Q R 12 cm 17 cm Example 3: Determine the measure of P. cos P = 0.70588 P = 45.1 P = cos –1 (0.70588) adjacent hypotenuse SOH CAH TOA
© The Visual Classroom Ex. 4: In PQR, Q = 90°. a) Find sin R if PR = 8 cm and PQ = 4 cm. R P Q 4 cm 8 cm b) Find cos R. RQ 2 = 8 2 – 4 2 RQ 2 = 64 – 16 RQ 2 = 48
© The Visual Classroom A B C Example 5: Determine the measure of B 3 cm opp ad j SOH CAH TOA 5 cm tan B = 1.6666 B = tan -1 (1.6666) B = 59.0°
© The Visual Classroom The slope of a wheelchair ramps is 1 12 What angle does the ramp make with the ground? A tan A = 0.0833 A = tan -1 (0.0833) A = 4.8° Ex 6:
© The Visual Classroom Ex. 7: From a distance of 20 m from the base a lighthouse the angle of elevation to the top of a lighthouse is 38º. Determine the height of the lighthouse. 38º h h = 20 tan 38° h = 20 (0.7813) h = 15.6 The lighthouse is 15.6 m high. 20 m h
by P Rowell Tile Hill Wood School
SOHCAHTOA TOA CAH SOH The three trigonometric ratios for right angled triangles are considered here. Click on a box to select a ratio.
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