Read the following study guide for a concept review:
Finding Angles in Right Triangles Study Guide
Practice Questions
1. 
A ship is 19 miles east and 52 miles south of its destination, as shown in Figure 15.6. What heading should the ship make to aim straight for its destination? 


2. 
A swimming pool is 30 feet long. It is 3 feet deep at the shallow end and 12 feet deep at the deep end. If the bottom of the pool is flat, as shown in Figure 15.7, what is the angle of its slope? 


3. 
A searchlight must monitor an 800foot prison wall. If the light is mounted 100 feet back from the middle of the wall, as shown in Figure 15.8, how many degrees of movement must it have? 


4. 
There are 15 feet of space to fit a ramp that must rise up the 2 feet 3 inches of a few steps. What would the angle of this ramp be? 
5. 
On one side of a street is a 250foottall building. Directly across the street, 100 feet away, a 320foottall building will be constructed. How much will the view of the smaller building be obstructed. In other words, what will be the angle from the top of the first building to the top of the second? 
6. 
Suppose regulations prohibit a car's headlights from aiming further than 100 feet up the road. If the headlights are 3 feet off the ground, what is the least angle below the horizontal that they may be aimed? 
7. 
A 3mileIong road winds down a hill that is 1,500 feet tall. If the slope of the road were constant, what would be the angle? (Hint: Use 1 mile = 5,280 feet.) 
8. 
A roof has a rise of 6 feet and a run of 15 feet. What is the angle of the roof? 
9. 
A moving truck comes with a 14footIong ramp. If the loading space is 3 feet off the ground, what will the angle of the ramp be? 
10. 
A spotlight is mounted 20 feet away from a mural. The light should shine at a spot 15 feet up the wall. At what angle should the spotlight be aimed? 
11. 
Suppose a 40foot tower is built to guard a gate that is 70 feet away. How many degrees below the horizontal is the direct path from the top of the tower to the gate? 
12. 
A 25footIong guide wire will be attached to the top of a 24foottall pole. What will be the angle between the wire and the pole? 
13. 
How much will a 40foot ladder lean if set 6 feet from the wall? That is, give the angle the ladder makes with the floor. 
14. 
A college student would like to launch a potato from his dorm window to one that is three stories higher (30 feet) in a building 35 feet away. What is the angle of the straight line between the two windows? 
15. 
Suppose a roof rises up a height of 15 feet as it runs horizontally 16 feet. What is the angle of the roof? 
16. 
Good drainage is provided when the ground slopes at 1 inch down for every 10 feet over. What angle is this? 
17. 
A diagonal board will be cut to fit into a rectangle that is 8 feet tall and 3.5 feet wide on the inside. At what angles should the ends of the board be cut? 
18. 
A diagonal board will be cut to fit into a rectangle that is 4 feet 2 inches by 3 feet 4 inches. At what angles should the ends of the board be cut? 
19. 
A ship is 4 miles off shore. Assuming that the shore is straight, what is the angle to a point 1.7 miles up the shore? 
20. 
A backyard loses 10 feet in elevation as it slopes down 22 feet (measured along the diagonal). What is the grade (the slope) of the ground? 
21. 
A video camera is set up 100 feet back from the center of a stage. Suppose the camera must be able to turn to point directly at any spot on the 4ofootwide stage. What is the largest angle that it must be turned to either side? 
22. 
A 3footwide door is attached to a doorway that is 1 foot 8 inches from a corner. How wide can the door be opened? That is, what is the measure of the obtuse angle when the door is opened widest? 
23. 
A woman stands in her yard. To the east is a stand of trees 30 feet tall and 25 feet away. To the west is her house, which is 40 feet tall and 35 feet away. How many degrees of sky can she see from where she stands? 
24. 
At what angle would you look up to see the top of a mountain if it has 2,000 feet more elevation than where you stand and is 2.3 miles away? 
25. 
A sloped driveway goes up 4 feet and is 22 feet long (measured along the diagonal ground). What is its grade? 
Answers
1. 
20° west of north 
2. 
16.7° 
3. 
76° in both directions, for a full span of 152° 
4. 
8.53° 
5. 
35° 
6. 
1.718° 
7. 
5.43° down 
8. 
21.8° 
9. 
12.37° 
10. 
36.87° up 
11. 
29.74° below the horizontal 
12. 
16.26° 
13. 
81.37° 
14. 
40.6° up from the horizontal 
15. 
43.15° 
16. 
0.48° 
17. 
66.37° and 23.63° 
18. 
51.34° and 38.66° 
19. 
23° 
20. 
27.04° 
21. 
11.3° 
22. 
123.75° 
23. 
81°, which remains when 50° and 49° are subtracted from 180° 
24. 
9.35° 
25. 
10.48° 
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