Expert: Richard J. Raridon - 3/18/2004

Question
1. part of a coaster track is straight andmakes an angle of 60 degrees with the horizontal. How far does the roller coaster drop when it travels 74 feet along this track?
2.You need the roof to have at least 45 degree slope. How long must the roof be if it is 40 feet from the center of the house to th eoutside wall?
3. a certain mountain is kmow to be 3 miles high. From yourlocation, you notice the angle of elevation is 15 degrees How far are you from the bottom of the mountain?
4. After hip surgery, a nurse elevated the patient's leg using a device that measures the degrees between the leg and the horizontal. If this device is set at 45 degrees and if it is 12 inches from the patients hip to knee, how high is the leg elevated?
5. to find the width of a river, a suryeor has measured the angle between the bank that he is on the other side. the angle is 75 degrees. The suryeor also knows a 16 yeard measure as shown below. Find the width of a river.
6. While riding in an airplane, you notice a city at an angle of depression of about 30 degrrees if the airplane is 10,000 ft. high, how far are you from the city?
7. a photographer wishes to take a pic. of a bird in a tree. She is 15 ft. from the base of the tree and is shooting at a 50 degree angle of elevation. How far is the camera from the bird?
8. A spy satellite 300 miles above the earth spots a mobile missile launcher directly below. At an angle of 0.095 degrees elevation the satellite also sees a hospital. What is the distance between the missile launcher and the hospital?
9. Consider location A and B on the surface of th eearth, approx. 2085 miles apar. The angle of elevation to the moon from location A is the elevation = 89.5 degrees. assuming that the moon is directly over location B find the dist. between the earth and the moon. Tan 89.5 deg. = 114.6
10. a 6 foot man casts a shadow 3.5 foot long. Finf the angle if elevation of the sun.
11. whil etraveling 1000ft. along a straight decling road, a car experiences a vertical drop of 174 ft. Find angle of elevation?
12. a ship is traveling 9 miles directly north of a lighthouse. Which direction must the ship travel in order to reach a port that is 3.3 miles west of the lighthosue?
13. A person in a wheelchair travels 30 feet along a ramp to reach an entrance that is 29 ft. from the sidewalk. How steep is the ramp.
14. while on a geology expedition. Greg and kate have run out of water. The temp. is 101 degrees F. and there are no trails According to their map, the nearest water source could be reached by travelign 3 miles south, then 2.5 miles east. They have a compass. Which direction should they tracel in  order to reach the water source as quickly as possible?
15. Karen writes computer programs for a company that makes video games. In a particular game, she needs the triangle shown below to appear on the screen. In order to program the triangle into the software, it is necessary for her to know angle of elevation. Find angle of elvation?

Answer
1. sin(60)=h/74, h = 64.1
2. length = 2(40)/cos45 = 113 feet
3. tan15 = 3/x, x = 11.3 miles
4. h = 12sin45 = 8.5"
5. shown below?
6. tan30 = 10000/x, x = 17,320 feet
7. cos50 = 15/R, R = 23.3 feet
8. tan(0.095) = x/300, x = 0.5 mile
9. distance = 2085tan(89.5) = 239,000 miles
10. tanA = 6/3.5, A = 60 degrees
11. tanA = 174/1000, A = 9.9 degrees
12. tanA = 3.3/9, A = 20.1 degrees west of south
13. cosA = 29/30, A = 14.8 degrees
14. tanA = 2.5/3, A = 40 degrees east of south
15. shown below?