1. A 37-ft pole casts a 21 ft. shadow. What is the angle of elevation of the sun?
A. 60°11'
B. 60°25'
C. 60°35'
D. 60°
Solution:
tanA = 37/21
A = arctan 1.7619047619047619047619047619048
A = 60.4221613187387
A = 60.42°
A = 60° 25' 19.78"
2. If a kite makes an angle of 39°30' with the level ground when a 460 feet of string is out. How high is the kite?
A. 292.6 ft
B. 292.59 ft
C. 292 ft
D. 292.5 ft
Solution:
sin39°30' = y/460
y = 460sin39°30'
y = 292.595981328 ft
y = 292.6 ft
3. A pilot on a plane saw a nearby island in front of him. If he is 2975 m above the ground and the horizontal distance of the island to the pilot 2345 m away. What is the angle of depression of the pilot to the island?
A. 51°45
B. 51°40'
C. 51°43'
D. 51°
Solution:
tanA = 2975/2345
A = arctan 1.2686567164179104477611940298507
A = 51.753574058883°
A = 51° 45' 12.87"
4. A boy is seen standing on the highest part of a mango tree. On top of the tree, he saw an observer looking at him 5 meters away. If the angle of depression of the boy to the observer is 34°26', what is the height of the tree?
A. 3.44 m
B. 3.4 m
C. 3.42 m
D. 3.43 m
Solution:
tan34°26' = h/5
h = 5tan34°26'
h = 5tan34.43333°
h = 3.4278453912 m
h = 3.43m
5. A man is seen on top of a coconut tree. 3 meters away from him is another coconut tree. On the bottom of the other tree, there is a fallen coconut. If the angle of depression of the man to the fallen coconut is 68°17', how high is the coconut tree that he is located?
A. 7.55 m
B. 8 m
C. 7.53 m
D. 7.5 m
Solution:
tan68°17' = h/3
h = 3tan68°17'
h = 3tan68.28333°
h = 7.5322872856
h = 7.53 m
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