Trigonometry Flashcards
Convert 405° to mils
a) 2,800
b) 7,200
c) 10,200
d) 6,200
b) 7,200
What is the equivalent of 9600 mils in centesimal system?
a) 600 grads
b) 700 grads
c) 800 grads
d) 900 grads
a) 600 grads
The supplement of an angle is thrice its complement. Find the angle.
45°
The sides of a right triangle measure 3, 4, and 5. Solve the interior angles of this triangle.
53.13°
36.87°
A surveyor can measure the width of a river by setting up a transit at a point C on one side of the river and taking a sighting of a point A on the other side. After turning through an angle of 90° at C, the surveyor walks a distance of 200 meters to point B. Using the transit at B, the angle is measured and found to be 20°.
What is the width of the river in meter?
72.79 m
A straight trail leads from the Alpine Hotel, elevation 8000 feet, to a scenic overlook, elevation 11,100 feet. The length of the trail is 14,100 feet.
What is the inclination (grade) of the trail?
12.70°
Adorning the top of the Board of Trade building in Chicago is a statue of Ceres, the Roman goddess of wheat. From street level, two observations are taken 400 feet from the center of the building. The angle of elevation to the base of the statue is found to be 55.1°, and the angle of the elevation to the top of the statue is 56.5°.
What is the height of the statue?
30.95 ft
A Boeing 777 aircraft takes off from O’Hare Airport on runway 2 LEFT, which has a bearing of N20°E. After flying for 1 mile, the pilot of the aircraft requests permission to turn 90° and head toward the northwest. The request is granted.
After the plane goes 2 miles in this direction, what bearing should the control tower use to locate the aircraft?
43.43°
A tree growing on hillside casts 10.2 meters shadow straight downhill. Find the vertical height of three if, relative to the horizontal, the hill slopes 15° and the angle of elevation of the sun is 62°.
a) 5.62 m
b) 19.18 m
c) 15.89 m
d) 5.42 m
c) 15.89 m
From the building across, the angle of depression of the base of the front edifice is 23.5° and the angle of elevation to the top is 52.78°. The height of observation is 14 m. What is the height of the edifice?
a) 56.4 m
b) 68.8 m
c) 76.6 m
d) 42.4 m
a) 56.4 m
Determine which quadrant the angle terminates given the conditions: secθ < 0 and tanθ > 0.
Quadrant III
If secx = 5/3 and x is in the fourth quadrant, what is the value of cscx?
-5/4
If cosθ = -15/17 and θ is in third quadrant, what is the value of 289sinθcosθ?
120°
Triangle ABC has the following data: b = 19 and A = 50°. How many triangles may be formed if:
a) a = 12?
b) a= 17?
c) a = 23?
a) no triangles
b) 2 triangles
c) 1 triangle
Solve the interior angles of the triangle with a = 3 ft, b = 4ft, and c = 6 ft.
A = 26.38°
B = 36.34°
C = 117.28°
A fire at F is spotted from two fire lookout stations, A and B, which are located 10.3 mi apart. If station B reports the fire at angle ABF = 52.6°, and station A reports the fire at angle BAF = 25.3°, how far is the fire from station A?
a) 1.72 mi
b) 7.44 mi
c) 4.50 mi
d) 8.37 mi
d) 8.37 mi
Cleveland, Columbus, and Toledo form a triangle in Ohio with Columbus 120 mi southeast of Toledo, and Cleveland 112 mi northeast of Columbus. If the angle at Toledo is 59.7°, how far is it from Toledo to Cleveland?
a) 124.96 mi
b) 103.08 mi
c) 127.56 mi
d) 119.04 mi
b) 103.08 mi
A ship sails 15.0 mi on a course S40°10’W and then 21.0 mi on a course N28°20’W. Find the distance (in mi) and direction (in degree minutes) of the last position from the first.
20.9 mi
N70°21’W
Coast Guard Station Zulu is located 120 miles due west of Station X-ray. A ship at sea sends an SOS call that is received by each station. The call to Station Zulu indicates that the bearing of the ship from Zulu is N40°E. The call to Station X-ray indicates that the bearing of the ship from X-ray is N30°W. How far is each station from the ship?
From Zulu: 110.59 mi
From X-ray: 97.82 mi
