# © The Visual Classroom Trigonometry: The study of triangles (sides and angles) physics surveying Trigonometry has been used for centuries in the study.

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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

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