Chapter 5

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. A 30 -foot-long driveway slopes downward at an angle of \(8^{\circ}\) with respect to the adjacent street. How far below the street is the lowest point of the driveway?

Use the negative-angle identities to compute the exact value of each of the given trigonometric functions. $$\sec \left(-\frac{4 \pi}{3}\right)$$

Convert the angle measures given in decimal degrees to DMS form. Round to the nearest second. $$53.5^{\circ}$$

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. The angles of depression of two points on the ground with respect to a hot-air balloon 2 miles up in the air are \(14^{\circ}\) and \(32^{\circ} .\) How far apart are the two points if they lie on a straight line that passes through the point on the ground that is directly below the balloon?

Use the negative-angle identities to compute the exact value of each of the given trigonometric functions. $$\csc \left(-\frac{5 \pi}{4}\right)$$

Convert the angle measures given in decimal degrees to DMS form. Round to the nearest second. $$87.5^{\circ}$$

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. The angle of elevation of the top of a hill with respect to a certain point on the surrounding level ground is \(10^{\circ} .\) If the hill is 9 feet high, what is the horizontal distance of the top of the hill from that point?

Use the negative-angle identities to compute the exact value of each of the given trigonometric functions. $$\tan \left(-\frac{7 \pi}{3}\right)$$

Convert the angle measures given in decimal degrees to DMS form. Round to the nearest second. $$40.25^{\circ}$$

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. A ramp makes an angle of \(15^{\circ}\) with the ground. If the top of the ramp is 4 feet above the ground, how long is the ramp?

Use the negative-angle identities to compute the exact value of each of the given trigonometric functions. $$\cot \left(-\frac{11 \pi}{6}\right)$$

Convert the angle measures given in decimal degrees to DMS form. Round to the nearest second. $$81.75^{\circ}$$

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. In Milwaukee, Wisconsin, the building code states that for a ramp to qualify as handicapped accessible, it can rise only 1 foot for every 8 feet of horizontal length. What is the degree of incline for the ramp to the nearest thousandth of a degree? (Source: www.mkedcd.org)

Find the exact value of each expression without using a calculator. $$\sin \frac{\pi}{2}+\cos \pi$$

Convert the angle measures given in decimal degrees to DMS form. Round to the nearest second. $$58.29^{\circ}$$

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. Sara wants to make a quilt square by using right triangles of varying colors. The triangles need to have an hypotenuse of length 10 centimeters. If the triangles are isosceles right triangles, what is the length of each side of the triangle to the nearest hundredth of a centimeter?

Find the exact value of each expression without using a calculator. $$\sin \frac{3 \pi}{2}+\cos \frac{\pi}{2}$$

Convert the angle measures given in decimal degrees to DMS form. Round to the nearest second. $$120.68^{\circ}$$

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. When the Eiffel Tower was dedicated in \(1889,\) its height (including the flagpole on top) was 324 meters. If the angle of elevation of the top of the tower from a certain point from the ground is \(50^{\circ},\) how far is the point from the center of the base? (Source: www.tour-eiffel.fr/teiffel/uk)

Find the exact value of each expression without using a calculator. $$3 \sin \frac{\pi}{4}+2 \cos \frac{3 \pi}{4}$$

In this set of exercises, you will use degree and radian measure to study real-world problems. What is the angle swept out by the second hand of a clock in a 10 -second interval? Express your answer in both degrees and radians.

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. From the south rim of the Grand Canyon near Grand Canyon Village, the vertical distance to the canyon floor is approximately 5000 feet. Standing at this point, you can see Phantom Ranch by looking down at an angle of depression of \(30^{\circ} .\) Find the distance to the camp, to the nearest foot, from the point at the base of the rim directly under where you stand. (Source: www.nps.gov/grcal)

Find the exact value of each expression without using a calculator. $$2 \sin \frac{\pi}{6}-\cos \frac{\pi}{3}$$

In this set of exercises, you will use degree and radian measure to study real-world problems. What is the angle swept out by the second hand of a clock in a 20 -second interval? Express your answer in both degrees and radians.

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. A security camera is mounted on the wall at a height of 10 feet. At what angle of depression should the camera be set if the camera is to be pointed at a door 50 feet from the point on the floor directly under the camera?

Find the exact value of each expression without using a calculator. $$\sin \frac{\pi}{4} \cos \frac{\pi}{4}$$

In this set of exercises, you will use degree and radian measure to study real-world problems. A robotic arm pinned at one end makes a complete revolution in 2 minutes. What is the angle swept out by the robotic arm in 1.5 minutes? Express your answer in both degrees and radians.

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. During a hike in Mexico, Sam discovered a large stone statue. To estimate the height of the object, he stood 20 feet from the statue and measured the angle of elevation to the top of the statue to be \(70^{\circ} .\) What is the height of the statue to the nearest foot?

Find the exact value of each expression without using a calculator. $$\sin \frac{\pi}{3} \cos \frac{\pi}{6}$$

In this set of exercises, you will use degree and radian measure to study real-world problems. A robotic arm pinned at one end makes a complete revolution in half a minute. What is the angle swept out by the robotic arm in 20 seconds? Express your answer in both degrees and radians.

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. Jake has a Surftech Softop surfboard. When he stands it up in the sand, it casts a shadow that is 84 inches long. If the angle of elevation of the sun is \(45^{\circ}\) how long is the board?

Find the exact value of each expression without using a calculator. $$\tan \frac{\pi}{4} \sec \frac{\pi}{4}$$

In this set of exercises, you will use degree and radian measure to study real-world problems. Earth makes one full rotation about its axis every 24 hours. How many degrees does Earth rotate in 1 hour?

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. The Great Pyramid of Giza in Egypt is 481 feet high. The distance from the point directly under the highest point to the edge of the pyramid is 375.5 feet. What is the angle of elevation of the sides of the pyramid?

Find the exact value of each expression without using a calculator. $$\cot \frac{\pi}{3} \csc \frac{\pi}{6}$$

In this set of exercises, you will use degree and radian measure to study real-world problems. Clocks Find the distance traversed by the tip of the minute hand on a clock between 5: 12 P.M. and 6: 27 P.M. on any given day if the length of the minute hand is 4 inches. Express your answer in inches.

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. A force \(\boldsymbol{F}\) can be decomposed into its horizontal component \(F_{x}\) and its vertical component \(F_{y} .\) The ratio of \(F_{y}\) to \(F_{x}\) is given by tan \(\theta,\) where \(\theta\) is the angle whose initial side is the positive \(x\) -axis and whose terminal side is oriented in the direction of \(\boldsymbol{F} .\) Find the value of that ratio if \(\theta=36^{\circ}\)

Find the exact value of each expression without using a calculator. $$\csc \frac{\pi}{2}-4 \cot \frac{\pi}{2}$$

In this set of exercises, you will use degree and radian measure to study real-world problems. In the 1800 s, women often carried pleated fans. One of the fans on display at the Smithsonian is 7 inches long and, when fully open, sweeps out an angle of \(80^{\circ}\) How long is the trim, to the nearest tenth of an inch, on the curved edge of the fan?

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. A piece of fabric that will serve as the background for a monogram on a sweater is to be cut in the form of a right triangle. What is the ratio of the lengths of the two shortest edges of the piece of fabric if one of the shortest edges is 3.5 inches long and the angle opposite that edge is \(45^{\circ} ?\)

Find the exact value of each expression without using a calculator. $$3 \tan \pi+5 \sec \pi$$

Sam has a fountain in his backyard. He has decided to make a bed of flowers around the fountain in the shape of a disc with diameter 6 feet. As a border around the bed, he is going to place shrubs around \(\frac{2}{5}\) of it and a stone border around the remaining part. How many feet of stone border does he need?

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. A surveyor stands 180 feet from the base of a building. The angle of elevation of the top of the building with respect to the location of the surveyor is \(57^{\circ} .\) Find the height of the building.

Find the exact value of each expression without using a calculator. $$\tan \frac{\pi}{3}-\cos \frac{\pi}{6}$$

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. The angle of depression of a certain point on the surface of the water in a swimming pool with respect to the end of the diving board is \(25^{\circ} .\) That point is at a horizontal distance of 15 feet from the end of the diving board. A 6 -foot-tall swimmer aims for the point in question and makes a straight-line dive, head first. If the top of his head makes contact with the water at that point, find the distance \(d\) traversed by his feet between the time they left the end of the diving board and the time his head hit the water. (IMAGES CANNOT COPY)

Find the exact value of each expression without using a calculator. $$\sin \frac{\pi}{6}+\cot \frac{\pi}{6}$$

Chicago, Illinois (\(42^{\circ}\) north latitude), is due north of Birmingham, Alabama (33" north latitude). If Earth's radius is approximately 3900 miles, find the approximate distance between the two cities, to two decimal places.

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. The Washington Monument in Washington, DC, is 555 feet high. If the angle of elevation of the top of the monument from a certain point on the ground is \(60^{\circ},\) how far is that point from the center of the base? Consider the base of the monument to be on the ground.

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. A 45 -foot-long hill makes an angle of \(20^{\circ}\) with the level ground at the bottom of it. After a big snowfall, people like to sled down the hill. How high above the surrounding level ground do they begin their descent?

A car with tires 24 inches in diameter travels at a specd of 60 mph. What is the angular speed of the tires? Express your answer in both degrees per second and radians per second.