GLEN-TRIGO

Question 1

1. Earth rotates once on its axis approximately every 24 hours. About how
   many degrees does a point on the equator travel through in one hour? in one
   minute? in one second?

Answer 1

ANS: 15°; 0.25°or 15’; 0.0042°or 15

Question 2

2. The angle of inclination of the sun affects the heating and cooling of
   buildings. The angle is greater in the summer than the winter.

A. The latitude of Brownsville, Texas, is 26°. Find the angle of inclination for
Brownsville on the first day of summer (day 172) and on the first day of winter
(day 355)

Answer 2

ANS: about 87.5°; about 40.5°

Question 3

B. The latitude of Nome, Alaska, is 64°. Find the angle of inclination for Nome
on the first day of summer and on the first day of winter

Answer 3

ANS: about 49.5°; about 2.5°

Question 4

C. Which city has the greater change in the angle of inclination?

Answer 4

ANS: neither

Question 5

3. The Ponce de Leon lighthouse in St. Augustine, Florida, is the second tallest
   brick tower in the United States. It was built in 1887 and rises 175 feet above
   sea level. How far from the shore is a motorboat if the angle of depression
   from the top of the lighthouse is 13° 15’?

Answer 5

ANS: about 743.2 f

Question 6

4. The escalator at St. Petersburg Metro in Russia has a vertical rise of 195.8
   feet. If the angle of elevation of the escalator is 10° 21 36 , find the length of
   the escalator.

Answer 6

ANS: about 1088.8 ft

Question 7

5. The longest truck-mounted ladder used by the Dallas Fire Department is
   108 feet long and consists of four hydraulic sections. Gerald Travis, aerial
   expert for the department, indicates that the optimum operating angle of this
   ladder is 60°.

A. How far from the building should the base of the ladder be placed to achieve
the optimum operating angle?

Answer 7

ANS: about 43.9 ft

Question 8

B. How far should the ladder be extended to reach the roof?

Answer 8

ANS: about 87.8 ft

Question 9

6. The Cape Hatteras lighthouse on the North Carolina coast was built in 1870 and rises 208 feet above sea level. How far apart are these vessels? Does the keeper
   have to sound the horn?

Answer 9

ANS: about 366.8 ft; no

Question 10

7. Latasha and Markisha are flying kites on a windy spring day. Latasha has
   released 250 feet of string, and Markisha has released 225 feet of string. The
   angle that Latasha’s kite string makes with the horizontal is 35°. The angle
   that Markisha’s kite string makes with the horizontal is 42°. Which kite is higher
   and by how much?

Answer 10

ANS: Markisha’s; about 7.2 ft

Question 11

8. A hot air balloon is flying above Groveburg. To the left side of the balloon,
   the balloonist measures the angle of depression to the Groveburg soccer fields
   to be 20° 15 .

A. Find the distance from the balloon to the soccer fields.

Answer 11

ANS: about 3.6 m

Question 12

B. What is the distance from the balloon to the football field?

Answer 12

ANS: about 1.4 mi

Question 13

9. In order to avoid a storm, a pilot starts the flight 13° off course. After flying
   80 miles in this direction, the pilot turns the plane to head toward the
   destination.
   A. What is the distance of the flight?

Answer 13

ANS: about 227.7 mi

Question 14

B. Find the distance of a direct flight to the destination.

Answer 14

ANS: about 224.5 mi

Question 15

10. An engineer designed three gears as shown at the right. What is the
    measure of theta?

Answer 15

ANS: about 100.6°

Question 16

11. The original height of the Leaning Tower of Pisa was 184 1/2 feet. At a
    distance of 140 feet from the base of the tower, the angle of elevation from the
    ground to the top of the tower is 59°. How far is the tower leaning from the
    original vertical position?

Answer 16

ANS: about 9.6°

Question 17

13. A fire is sighted from a fire tower in Wayne National Forest in Ohio. The
    ranger found that the angle of depression to the fire is 22°. If the tower is 75
    meters tall, how far is the fire from the base of the tower?

Answer 17

ANS: about 185.6 m

Question 18

14. In baseball…, The distance between
    consecutive bases is 90 feet. In Wrigley Field in Chicago, dead center field is
    400 feet from home plate. How far is dead center field from first base?

Answer 18

ANS: about 342.3 ft

Question 19

15. The distance between Miami and Orlando is about 220 miles. A pilot flying
    from Miami to Orlando starts the flight 10° off course to avoid a storm.

A. After flying in this direction for 100 miles, how far is the plane from Orlando?

Answer 19

ANS: about 122.8 mi

Question 20

B. If the pilot adjusts his course after 100 miles, how much farther is the flight than a direct route?

Answer 20

ANS: about 2.8 mi

Question 21

16. A soccer player is standing 35 feet from one post of the goal and 40 feet from the other post.If the goal is 24 feet wide,
    which player has a greater angle to make a shot on goal?

Answer 21

ANS: the player 30 ft and 20 ft from the posts

Question 22

1. Earth rotates once on its axis approximately every 24 hours. About how many degrees does a point on the equator travel through in one hour? in one minute? in one second?

Answer 22

ANS: 15°; 0.25°or 15’; 0.0042°or 15

Question 23

2. The angle of inclination of the sun affects the heating and cooling of
   buildings.
   A. The latitude of Brownsville, Texas, is 26°. Find the angle of inclination for
   Brownsville on the first day of summer (day 172) and on the first day of winter
   (day 355).

Answer 23

ANS: about 87.5°; about 40.5°

Question 23

2. The angle of inclination of the sun affects the heating and cooling of
   buildings.

B. The latitude of Nome, Alaska, is 64°. Find the angle of inclination for Nome
on the first day of summer and on the first day of winter.

Answer 23

ANS: about 49.5°; about 2.5°