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From a point 48 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 56

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From a point 48 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 56.3°. Find the height of the tree to the nearest foot. Show work. (sketch is not to scale) 56.30 48 feet 26. For the triangle ABC, we are given that A = 42°, B = 58°, and c = 16.0. a 42° 58° C= 16 B Find the length of side a, rounded to the nearest tenth. Show work. 27. Let ?= (16, 4) and 7 = (2,-8). (b) Calculate the dot product ?.õ. Show work. (c) Determine the angle between û and 7. Round the result to the nearest degree. Show work. (x - 8), (y + 1)2 + -= 1 28. An ellipse has the equation 16 100 (a) Is the major axis horizontal or vertical? (b) Find the exact values of the foci of the ellipse. Show work. Page 7 of 7 18. Find the equation for a line which passes through the points (5,2) and (7,-8). Write the equation in slope-intercept form. Show work. 19. Find the exact solutions and simplify as much as possible: 2x = 7+ 4x. Show work. 20. Letf(x) = 3x² - 4 and g(x) = x-3. (a) Find the composite function (fog)(x) and simplify. Show work. (b) Find (fog)(-2). Show work. 21. A projectile is launched from a platform 12 feet high with an initial velocity of 72 feet per second, The height h of the projectile at t seconds after launch is given by h=-167 + 72t + 12 feet. (a) How many seconds after launch does the projectile attain maximum height? Show work. (6) What is the maximum height? Show work. 22. Solve: x+7 24 + =0. Show work. x+3 x2-9 23. Suppose that sin 0 = 4/5 and that is a Quadrant II angle. (a) Find the exact value of cos O. Show work. (b) Find the exact value of sin(28). Show work. 24. Prove the identity (cos x – sin x)² + sin(2x) = 1 Page 6 of 7 10. A can of soda at 82° F. is placed in a refrigerator that maintains a constant temperature of 35° F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by -0.058 t T(t) = 35 + 47 e Find the temperature of the soda 10 minutes after it is placed in the refrigerator. (Round to the nearest degree.) Answer: 5 11. Given the function f(x) x, find a formula for the inverse function. Answer: 12. (a) State the reference angle associated with 120°. Answer: (b) Convert 225º to radians. Leave the answer in terms of it. Answer: 13. Given y = 5 sin(8x – 1), state the (a) period Answer: - (b) phase shift Answer: 14. Solve the trigonometric equation (cos x)(2 sin x - 1) = 0 in the interval [0, 360°). Answer: 2 TT 15. Answer: W (a) Find the exact value of arcsin (sin 5) (b) Find the exact value of arccos (tan s (tan) Answer: 16. For the parabola given by (x – 3)2 = 8(y + 8), find the following: (a) direction parabola opens (to the left, right, up, or down) Answer: Answer: (b) vertex Answer: (c) focus Page 4 of 7