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Warm-Up: Solve each equation in your notebook 1) x 0.875 18 2) 24 0.5 y 3) y 0.96 25 4) 0.866x = 12 5) 0.5x = 18 1) 2) 3) 4) 15.75 48 24 13.9 5) 36 Students will define sine, cosine, and tangent ratios in right triangles. Trigonometric Ratios The relationships between the angles and the sides of a right triangle. Trignometric Ratios How do I remember this? Three basic ratios: • sine (sin), cosine (cos), tangent (tan) Trigonometric Ratios Theorem Let ABC be a right triangle. The sine, the cosine, and the tangent of the acute angle A are defined as B follows: a opposite sin A = c hypotenuse cos A = tan A = adjacent hypotenuse opposite adjacent c b c a b A a b C It is known that a hill frequently use for sled riding has an angle of elevation of 300 at its bottom. If the length of a sledder’s ride is 52.6 feet estimate the height of the hill. h sin 30 52.6 52.6 0 52.6 sin 30 h (52.6) (0.5) h 0 26.3 h h 300 You want to find the height of a tower used to transmit cellular phone calls. You stand 100 feet away from the tower and measure the angle of elevation to be 400. How high is the tower? t tan 40 100 0 tower 100 tan 40 0 t (100) .8391 t 84 ft t you 400 100 ft Practice Time! sin A 12 .8 15 x sin 50 15 x 11.5 cos A 9 .6 15 sin B 9 .6 15 cos B 12 .8 15 5 cos63 x x 11 x cos 38 21 x 16.5