ο·Chapter Three: Right Triangle Trigonometry ο· The Tangent Ratio (3.1) In the last lesson we talked about the ratios: B opp sinA = opp hyp cos A = adj hyp Quad II Quad I Quad III Quad IV hyp C adj A Is there another ratio we could make? opp/adj tangent ratio: for an acute angle in a right triangle, the ratio of the length of the πππ opposite side to the length of the adjacent. tan A = ππ π primary trigonometric ratios: are the three ratios, sine, cosine and tangent defined in a right triangle. SOH CAH TOA eg #1 Determine the ratio to four decimal places and list the quadrant where the angle is found. a. tan 23°= 0.4245 and it lies in Quadrant I . b. tan 98°= -7.1154 and it lies in Quadrant II . c. tan 123° = -1.5399 and it lies in Quadrant II . d. tan 224°= 0.9657 III . e. tan 330°= -0.5774 and it lies in Quadrant and it lies in Quadrant IV . eg #2 What is the measure of the angle to the nearest degree if the following ratios are known? a. tan Σ¨ = 1.3270 Σ¨ = 53ο° b. Σ¨ = 25ο° tan Σ¨ = 0.4663 c. tan Σ¨ = 2.1445 Σ¨ = 65ο° eg #3 What are the measures of the unknown sides and angles, (solve the triangle). **Three angles of a triangle = 180ο° Pythagorean Theorem: c2 = a2 + b2 a. b. 12 mm ο± ο± 5 mm c2 = a2 + b2 c2 = 52 + 122 c = 13 mm 13 ft c2 = a2 + b2 c2 = 132 + 82 c = 15.2 ft 8 ft tan ο± = πππ ππ π tan ο‘ = πππ ππ π tan ο± = πππ ππ π tan ο‘ = πππ ππ π tan ο± = π ππ tan ο‘ = ππ π tan ο± = π ππ tan ο‘ = ππ π ο ο± = 23ο° ο ο‘ = 67ο° ο ο± = 32ο° ο ο‘ = 58ο° eg #4 From the top of a building 35 m tall, the angle of elevation to the top of a taller building is 35ο°. The distance between the buildings is 43 m. What is the height of the taller building? x 35ο° 43 m 35 m tan ο± = πππ ππ π tan 35ο° = π ππ x = tan 35ο° x 43 x = 30.1 m Assign: p.108-110 #3-9, 11, 13 height of taller building: 35 m + 30.1 m = 65.1 m