Please solve both subparts. ets6 Applications of Trigonometry in 3-dimensional Problems6.In the figure, TA is a vertical building of height 60 m. A, B and Care points on the horizontal ground. B is 24.6 m due south of A80°and BC = 20 m. The angle of depression of C from T is 80°. Find%3D60(a) the distance between A and C,(b) the true bearing of C from A.>ESolution24.6 mB 20 m(a)(b)

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Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter7: Triangles

Section7.1: The Law Of Sines

Problem 36PS

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Distance and Bearing Problems 27 through 32 involve directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line. A man wandering in the desert walks 2.3 miles in the direction S 310 W. He then turns 90 and walks 3.5 miles in the direction N 59 W. At that time, how far is he from his starting point, and what is his bearing from his starting point?
Shooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the path of a projectile with initial speed v0=32ft/s, fired into a headwind of =24ft/s, for the angles =5,15,30,40,45,55,60 and 75. Is it still true that the greatest range is attained when firing at 45 ? Draw some more graphs for different angles, and use these graphs to estimate the optimal firing angle.
Rescue A helicopter makes a forced landing at sea. The last radio signal received at station C gives the bearing of the helicopter from C as N 57.5 E at an altitude of 426 feet. An observer at C sights the helicopter and gives DCB as 12.3, how far will a rescue boat at A have to travel to reach any survivors at B (Figure 20)? Figure 20
Distance and Bearing Problems 27 through 32 involve directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line. Lompoc, California, is 18 miles due south of Nipomo. Buellton, California, is due cast of Lompoc and S 65 E from Nipomo, how far is Lompoc from Buellton?
Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The first gear in a single-stage gear train has 42 teeth and an angular velocity of 2 revolutions per second. The second gear has 7 teeth. Find the angular velocity of the second gear.
Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The second gear in a single-stage gear train has 6 teeth and an angular velocity of 90 revolutions per minute. The first gear has 54 teeth. Find the angular velocity of the first gear.
Softball and Rectangular Coordinates If a coordinate system is superimposed on the softball diamond in Problem 42 with the origin on home plate and the positive x-axis along the line joining home plate to second base, what would be the coordinates of first base and third base?
Laying Phone Cable City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank 5 miles down the river. You will lay L miles of the cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. See Figure 2.108. Figure 2.108 You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the Pythagorean theorem, relates the lengths of the three sides: Lengthofhypotenuse=Lengthofoneleg2+Lengthofotherleg2 a. Find an appropriate right triangle that shows that W=1+(5L)2 b. Find a formula for the length of the total phone cable P from City A to City B as a function of L. c. Make a graph of the total phone cable length P as a function of L, and explain what the graph is showing. d. What value of L gives the least length for the total phone cable? Draw a picture showing the least-length total phone cable.

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