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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 66

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 66. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | 20.1 Right-Triangle Trigonometry The Definitions 631 Trigonometry of Right Triangles From times of antiquity scientists and engineers have used triangle trigonometry to construct edifices and to estimate distances and heights from estimating the height of the great Egyptian pyramids in Giza to estimating the sizes and distances of the sun and the moon. A triangle has three sides and three angles. To solve a triangle means to find measures for all three sides and all three angles from information given. In the case of a right triangle if we know the measure of one of the acute angles then we know the measures of all the angles. This together with the length of any one side enables us to solve the triangle. If the lengths of any two particular sides of a right triangle are known we can use the Pythagorean Theorem to determine the length of the third and trigonometry to determine the measure of the angles. Knowing the measures of all three angles does not determine the triangle but knowing the length of all three sides does.5 Think about why this is so. Examples involving solving right triangles often include the terms angle of elevation and angle of depression. Angle of elevation refers to the angle from the horizontal up to an object angle of depression refers to the angle from the horizontal down to an object. EXAMPLE 20.1 A little girl flying a kite on a taut 350-foot string asks her father for the height of her kite. Her father estimates the angle of elevation of the kite to be 55 . Give an estimate for the height of the kite. Assume that the girl is holding the string 3 feet above the ground and her father is measuring the angle of elevation from this height. Figure 20.7 5 To determine a triangle means that these specifications determine all three sides and all three angles. 632 CHAPTER 20 Trigonometry Circles and Triangles SOLUTION Let x 3 the height of the kite. We re looking for a trigonometric function that relates x and the known parts of the triangle. x is