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5.2 Apply the Tangent Ratio p. 157 Vocabulary Trigonometry: branch of mathematics that deals with the relationships between the sides and angles of triangles and the calculations based on these relationships Trigonometric ratio: ratio of lengths of 2 sides in a right triangle B C A Vocabulary OPPOSITE – Across from HYPOTENUSE – Side across from Rt Angle ADJACENT – Next to (not the Hypotenuse) B C A 3 Trig Ratios… Tangent (TAN) – ratio of the length of the opposite side to the length of the leg adjacent to the angle. We’ll learn about Sine (SIN) and Cosine (COS) in Section 5.3 Here’s how we remember it… SOH CAH B TOA C A TANGENT (TAN) tan A leg OppositeA BC leg Adjacent A AC B C A EXAMPLE 1 Find tangent ratios Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four places. SOLUTION tan S = opp S = RT = 80 ST 18 adj. to S = 40 9 4.4444 tan R = opp R = ST = 18 RT 80 adj. to R = 9 40 = 0.2250 GUIDED PRACTICE for Example 1 Find tan J. Round to four decimal places. ANSWER 0.7500 ANSWER 0.5333 EXAMPLE 2 ALGEBRA Find a leg length Find the value of x. SOLUTION x 32 24 ft EXAMPLE 2 ALGEBRA Find a leg length Find the value of x. SOLUTION 25 32 x CLASSWORK p. 159 #’s 1-6, 11-13 EXAMPLE 3 Estimate height using tangent LAMPPOST Find the height h of the lamppost to the nearest inch. opp. tan 70o = adj. h 40 tan 70o = 40 tan 70 o 109.9 Write ratio for tangent of 70o. Substitute. = h h Multiply each side by 40. Use a calculator to simplify. ANSWER The lamppost is about 110 inches tall.