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MAT 124 Spring 07 Dr. Hamblin Section 4.3: Right Triangle Trigonometry In the following triangles, evaluate the six trigonometric functions at the indicated angle θ. 1. 2. 3. Why were your answers to problems #1 and #2 the same? 4. Given sin θ = 3/4, construct an appropriate right triangle that has θ as one of its angles. Use the Pythagorean Theorem to find the third side of this triangle, and then evaluate the remaining five trigonometric functions of θ. 5. You are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 degrees. If the total height of the building is another 123 meters above the 86th floor, what is the approximate height of the building. MAT 124 Spring 07 Dr. Hamblin 6. In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive 13 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of the mountain. (Hint: Let the height of the mountain be x, and set up trigonometric equations from two triangles.) Solutions 1. 2. 3. 4. 5. 6. sin θ = 1/3, cos θ = 8 /3, tan θ = 8 /8, sec θ = 3 8 /8, csc θ = 3, cot θ = 8 . sin θ = 1/3, cos θ = 8 /3, tan θ = 8 /8, sec θ = 3 8 /8, csc θ = 3, cot θ = 8 . The triangles are similar, so the measure of θ is the same for both triangles. cos θ = 7 /4, tan θ = 3 7 /7, sec θ = 4 7 /7, csc θ = 4/3, cot θ = 7 /3. 443 meters 1.3 miles